Is there a prohibition to pick ones nose on shabbos assuming you won’t cause bleeding? What if often (but not always) the hairs come out as well (unintentionally)?
Shulchan Aruch writes regarding a similar case that if hairs will almost definitely come out, it is forbidden (1). Usually though, it would be allowed, as the chances of the hairs being pulled out is not ‘almost definite’. However, one should be careful to try not to pull out hairs. The mucus should be discarded immediately, as once it leaves the body it is considered muktza (2).
All the best
(1) Shulchan Aruch O:C 328:49, Mishna Berura ibid se’if katan 151.
(2) Shmiras Shabbos K’hilchaso 14:69.