Will mouse traps snap on cats?

I found evidence of mice (or mouse) in my lower cabinet. I have cats but with the cabinet doors closed, it’s understandable how they did not get the mouse.

I cleaned out the cabinet, am taking care of food storage for the future, and am going to leave the cabinet doors open with cabinet empty for a few days so the cats can explore in there and do their job.

I am going to buy mouse traps today. I figure it gives the cats backup.

Will mouse traps snap on cats? I am concerned if the cats go in the cabinet and sniff the trap, the trap will snap on them. Not that I think the mouse trap will kill the cat, because I know their big heads won’t fit in the trap, but I don’t want their paw or nose to get injured.