Parachute cord can be used as PART of a snare- but metal fishing line is for the part that catches the animal- they will chew thru 550 cord. Learn how to fashion an A trigger- uses a forked branch, notched on inside of fork, stick across the opening.
To be perfectly honest, the best traps are going to be made for that purpose- victor or conibear steel traps, or box traps for rabbits. Please be aware that if the world ain't done ended yet, trapping is regulated by state game laws, and needs a license.
As far as man traps- sorry bro, but in good conscience, I do not post instructions on building things like that on forums that can be accessed by 10 yr olds. Yeah, I know the info is out there- hell, watch the military channel- but I am not gonna be the one to post it.