It is fairly obvious that stitching a wound on shabbos is an issur d'oraysa. Although the melacha of tofer may not apply to human skin, but there is definitely an issur of chavala because each stitch makes a minor needle hole. Rav Shlomo Zalman (Minchas Shlomo 2:34:32) suggests that it may even be a Torah violation of Sewing. Being that we find in Rashi by bursting a pimple to make a pesach would be considered bo'neh (107a), it is also plausible that tofer applies to human skin. His reservation is that since the two parts of the skin are still alive and will ultimately grow together, it isn't considered detached so that the attaching through stitching would constitute a melacha of tofer.
R. Menachem Levine pointed out to me that the Nishmas Avrohom cites Rav Shlomo Zalman who a physician to stitch more than is necessary to close the wound, simply for the purpose of obtaining a more aesthetically pleasing result (the use of more stitches will make it heal nicer). The source of this ruling is based on the braisa that says that one who is doing a bris may cut the tzitzin that are not essential, so long as they haven't been פירש, meaning that they are still involved in the act of stitching. Just as by a bris, we allow one to cut more than is necessary for the bris to be kasher, and the rationale is as rashi explains דכולא חדא מילתא היא, so too when one needs to stitch for pikuach nefesh, they can stitch more than is absolutely necessary based on the same rationale. The license to cut ציצין שאינן מעכבין so long as one is still involved in the act, has nothing to do with הידור מצוה, rather it is because once he begins he has a right to do more than is absolutely necessary. The Nishmas Avrohom seemed to have misunderstood Rav Shlomo Zalman because he writes something about hidur mitzvah. The concept of hidur mitzvah is only necessary to explain why it may be even permitted to go back and cut once one has completed what they intended to do - פירש. Had this been the heter for cutting tzitzin even before one was פירש, it would certainly not be a source applicable to stitching a wound on shabbos.
I found that this approach of Rav Shlomo Zalman is printed in Minchas Shlomo 2:34:32,33. In the subcategory 32 (end of teshuva) he simply refers to the gemara by milah and draws a parallel to stitching more than necessary. In subcategory 33 he writes that the advantage of going back to cut ציצין שאינן מעכבין is for hidur, but he doesn't mean to say what the Nishmas Avrohom understood. The reason why it isn't considered a chilul shabbos to cut more than absolutely necessary is because it is all being done within the same act, not because one can be mechalel shabbos for hidur. But the reason we consider there to be an advantage to cut more tzitzin is because of hidur. Similarly for stitching, the heter is that it is all being done in the same act, but the reason we consider it to advantageous is because it will save him from lifelong embarrassment. In short, the heter is only based on it all being one act, but there needs to be a sevara why the extra stitches are considered one act and that is because just as for mila the hidur makes it considered the completion of the mitzvah, so too here the fact that there is a purpose in stitching more allows it to be considered the completion of what was started. That is why one would not be able to do extra stitches that would not accomplish anything, even if they haven't been פירש.
R. Menachem Levine pointed out to me that the Nishmas Avrohom cites Rav Shlomo Zalman who a physician to stitch more than is necessary to close the wound, simply for the purpose of obtaining a more aesthetically pleasing result (the use of more stitches will make it heal nicer). The source of this ruling is based on the braisa that says that one who is doing a bris may cut the tzitzin that are not essential, so long as they haven't been פירש, meaning that they are still involved in the act of stitching. Just as by a bris, we allow one to cut more than is necessary for the bris to be kasher, and the rationale is as rashi explains דכולא חדא מילתא היא, so too when one needs to stitch for pikuach nefesh, they can stitch more than is absolutely necessary based on the same rationale. The license to cut ציצין שאינן מעכבין so long as one is still involved in the act, has nothing to do with הידור מצוה, rather it is because once he begins he has a right to do more than is absolutely necessary. The Nishmas Avrohom seemed to have misunderstood Rav Shlomo Zalman because he writes something about hidur mitzvah. The concept of hidur mitzvah is only necessary to explain why it may be even permitted to go back and cut once one has completed what they intended to do - פירש. Had this been the heter for cutting tzitzin even before one was פירש, it would certainly not be a source applicable to stitching a wound on shabbos.
I found that this approach of Rav Shlomo Zalman is printed in Minchas Shlomo 2:34:32,33. In the subcategory 32 (end of teshuva) he simply refers to the gemara by milah and draws a parallel to stitching more than necessary. In subcategory 33 he writes that the advantage of going back to cut ציצין שאינן מעכבין is for hidur, but he doesn't mean to say what the Nishmas Avrohom understood. The reason why it isn't considered a chilul shabbos to cut more than absolutely necessary is because it is all being done within the same act, not because one can be mechalel shabbos for hidur. But the reason we consider there to be an advantage to cut more tzitzin is because of hidur. Similarly for stitching, the heter is that it is all being done in the same act, but the reason we consider it to advantageous is because it will save him from lifelong embarrassment. In short, the heter is only based on it all being one act, but there needs to be a sevara why the extra stitches are considered one act and that is because just as for mila the hidur makes it considered the completion of the mitzvah, so too here the fact that there is a purpose in stitching more allows it to be considered the completion of what was started. That is why one would not be able to do extra stitches that would not accomplish anything, even if they haven't been פירש.
However, the assumption that stitching is necessary for pikuach nefesh seems very strange. Unless we're dealing with a gunshot wound or something extremely major, it is almost always possible to stop the bleeding without stitching by either pressure, or other forms of chemicals that help coagulate the blood. If so, it would not be permitted for someone who is capable of stopping the bleeding at home to travel to drive to a hospital on shabbos in order to stitch a wound. The aesthetic advantage to stitching would certainly not justify a chilul shabbos of a Jew (for a Jew to be driven by a goy would certainly be okay to help a child who is injured, and perhaps even for an adult who is injured). Furthermore, it should be forbidden for a Jewish physician to stitch an open wound on Shabbos if he has the ability to stop the bleeding without violating Shabbos. Actually, Rav Shlomo Zalman addresses this as well and says that the aesthetic consideration would only justify chilul of a goy, not of a Jew (subcategory 33).