Yevamos 105a - Chalitzah with Left Hand and Teeth

Tosafos explains that just as the gemara allows chalitzah to be done with her teeth, it would also be allowed with her left hand, so the yerushalmi (quoted in Tosafos 102a bottom) that chalitzah should be with the right hand, is only lechatchila. However, Tosafos in Chulin 20a d.h. lo, entertains the possibility that although chalitzah cannot be done with the left hand, it still can be done with the teeth. What would be the logic to say that the left hand is worse than using teeth? It would seem that the heter of using teeth is only for one who does not have hands (as is mefurash in the gemara). For such an individual the teeth would be the way they move things around and do everything and would therefore become their "hands", but someone who has a right hand, only his right would qualify as his normal way of moving things and therefore we would require him to use his right hand. Based on this, if his right hand would be cut off, his left hand becomes like his right hand and he must then use his left hand and not his teeth.

However, this doesn't seem to fit into Tosafos in Chulin since Tosafos wants to prove from here that melika (shechting a bird) with his left hand may be worse than teeth. Tosafos seems to understand that even though we are not refering to someone missing hands (bec. that would render the kohein a ba'al mum) still there is some rationale that teeth would be better than the left hand! What is the rationale?