The gemara says that for a woman to transport oil using her hair would be better than carrying it in a jar because it would be a carrying with a shinuy thereby reducing the severity of the issur. The gemara asks that by carrying the oil absorbed in her hair, she will need to squeeze it out for the woman in labor to use thereby violating the prohibition of sechita so there is nothing gained by transporting the oil using her hair? The gemara answers אין סחיטה בשער meaning that there is no violation by squeezing the oil out of hair. Rashi seems to indicate that the question of the gemara is that squeezing the oil out of her hair would be a Torah violation. She would be avoiding the Torah violation of carrying but transgressing the Torah violation of squeezing so that nothing is gained! The gemara answers that since hair is hard and doesn't absorb (rashi), it would not be a Torah violation to squeeze the oil out of her hair.
It isn't clear from the gemara whether squeezing the oil out of the hair would still be a Rabbinic violation. It is possible that the gemara is saying that it is better to violate the issur d'rabonon of carrying with a shinuy and the issur d'rabonon of squeezing hair, rather than the Torah violation of carrying without a shinuy. But it is also possible that the gemara is saying that hair doesn't absorb so there is no issur at all to squeeze oil out of hair.
The Ran (Chiddushei Ha'Ran) proves from our gemara that it must at least be an issur d'rabonon. Being that carrying oil in hair is a greater shinuy than carrying on one's hand, why does the braisa prefer carrying the oil on one's hand over hair? It must be because carrying in the hair would require a second issur d'rabonon of squeezing. The Ran therefore holds that although there is no issur d'oraysa to squeeze hair, it is still assur d'rabonon because of מחזי כסחיטה therefore they were go'zer that if it is allowed one will come to squeeze.
The type of sechita that we are speaking about in this gemara is presumably the type of sechita that is related to מפרק which is a toldah of דש. The purpose of the sechita is to squeeze the oil for it's use, similar to the squeezing of a fruit for it's juice. It doesn't seem to be related to the sechita of מלבן since hair is not a garment for which there would be an issur of cleansing. When it comes to the type of sechita that is related to דש, we find a leniency when the liquid being squeezed out is ruined and wasted as it is squeezed out. The rationale is that when the liquid is wasted it is a מלאכה שא"צ לגופה and only assur m'drabonon (Shulchan Aruch 320:7). Based on this, the Shemiras Shabbos KiHilchasa (page 151) in footnote 64 cites Rav Shlomo Zalman as permiting on who's hair was wet to dry it with a towel. The rationale is that squeezing hair is only d'rabonon (and the fact that there is even an issur d'rabonon is not explicit in the gemara), and squeezing in a way where the liquid is wasted is only d'rabonon, therefore it is a double d'rabonon. Furthermore, he says that since the liquid is never ever realized or seen, it is immediately absorbed in the towel, it is not at all similar to the sechita that would be a tolda of דש.
However, the Rambam in Hilchos Shabbos (9:11) writes in the context of מלבן which is cleansing -
שהסחיטה מצרכי כיבוס הוא כמו שההגסה מצרכי הבישול, ואין סחיטה בשער וה"ה לעור שאין חייבין על סחיטתו
The language of the Rambam seems to imply that sechita on hair would be related to cleansing and one could deduce from the Rambam that it would be an issur d'rabonon. The Biur Halacha 302:9 d.h. assur seems to assume that the issur is a melabein related issur and is assur m'drabonon. If this were the case, there would be no leniency for being הולך לאיבוד, but the shemiras shabbos cites poskim who reject this assumption. Furthermore, the language of the Rambam actually implies that on skin there is sechita d'rabonon but on hair there is no sechita at all.