I've just been through this with the Xbow I've built... nightmare to string. The bracing/stringer/cocking string needs to be made of some decent non stretch material. I used an old crossbow string in the end.
Paracord is stretchy isn't it? (as it's designed to absorb shock). I'd look for some decent hemp cord/rope, I've used that for warbow stringers, a bit of initial stretch then it settles down.
Del
PS, I just looked at cheaprope.co.uk they have some interesting looking sash cord, unfortunately, no breaking strain figures
Toolstation do 10m of sash cord for less than 4 quid, and as it's made to run over a pulley it should be good.