I can't source this, but I would imagine that it would depend on whether or not the person holding the animal jumped -- see שמלה חדשה at 23:6, where he says that even where the שוחט cut his own finger, we are only worried where he noticed the cut before he finished שחיטה, and then only when he jumped.
As to the person holding the animal, he needs to hold it steady -- if it was not held steady, then there is a chashash of shehiyah, chalada. If his finger was cut, I would think he is not better or worse than the shochet himself.
Edit: When I wrote this answer, I had forgotten about what the Matteh Asher had written, ad loc 17 --
אם שחט בעצבאו של האוחט הבעל חי, כשר בכל ענין, שאין השוחט נבעת
if the knife cuts the finger of the guy holding the animal, then the שחיטה is absolutely kosher (because there is no reason for the שוחט to jump at that)
[ It should be noted that if the finger nail of the אוחז (or, indeed, that of the שוחט himself, יש להחמיר (but if they are absolutely certain that when the fingernail was cut, all cutting for the שחיטה stopped [and רוב was already achieved], one could be מיקל בהפסד מרובה) ]