missmouse,
Sometimes,a question comes along to which there is no easy answer.What kind of tiles are they,porcelain,ceramic,marble? Either way it will be tricky.As you say the wires are the problem.You would also have to watch out that don't loosen other tiles round about the cracked one.If you were to attempt to take it out,you should remove all the grout around the tile first,and then carefully chip away at the tile all around the edges,working towards the centre with say, a "smallish" screwdriver or wood chisel,nothing too heavy,and tapping with a hammer just enough to break bits off.Maybe once you can see the wires,it might make it a bit easier.I don't envy you in your task.Anyway,good luck.
Roughcaster.