it looks like that wire is just a spring alingner?... just pull it out... there are probably 3 or 4 that run along the bottom of the seat and they keep the springs tied together and evenly spaced.... I pulled 2 or 3 out of my seat each time they did that, just pulling out that one shouldn't make much difference....
If you don't want to pull it out, take a pair of pliers, compress the seat w/ some weight and bend the tip of the wire over on it self, back maybe an inch. When you let you let the weight off the seat, the wire should be short enough to hide inside the foam....and not poke you....
then you've got some more time to think about getting it recovered...