I've done this, and it works. Like a 4" diameter cookie-cutter through 1/4" plywood at 50 yards.
I first read about it in Kurt Saxon's The Weaponeer. Also recall seeing it loaded in some movie in the 80's or 90's.
But there are a number of practical problems to overcome:
1. Putting the wire through the shot. Either you'll have to drill the shot, buy some sort of pre-drilled shot (probably not lead shot in that case), or cast the shot around the wire. You can also buy "split shot" for fishing line, which is lead shot that is made with two joined halves that you simply clamp around fishing line. Not as aerodynamic, but usable.
2. Fixing the shot to stay in place along the wire. You can tie it in place (knots on either side), glue it, or rely on the clamping force alone of split shot.
3. Packing the wire into the shell. Strong wire is surprisingly stiff when you go to cram it into a shotgun shell. It ends up taking up a lot of volume, which reduces your pellet load. Weaker, but softer and more flexible wire, such as picture hanging wire, would probably be optimum.
IMHO casting the shot around flexible steel wire would work the best.