Wire EDM's do not plunge cut. The wire is on two spools, much like a tape recorder. The wire is fed past the work to make the cut. It is only used once as the process erodes the wire so it is unsuitable for a second pass. IIRC, .010" is about as small a wire that can be used although my experience goes back a decade.I'd suggest homebrew EDM; copper, graphite, and tungsten all make good durable cutters
for spark machining. Tungsten that thin, though; maybe a cheese-knife style cutter rather
than a stiff-wire plunge tool?
I made one using wire feed wire and it worked well. The biggest problem I had was when I applied enough tension to keep the wire taught, the wire would break if the wire got too hot. Tungsten should work better in that regard.Hot wire foam cutter