Of course the wireless soulution will work, just keep some things in mind....
I am guessing that the ps2 requires a cat5 cable, not jacking the cable right in there, so if this is the case, all you would need is a Linksys 2 prt wireless router and one wireless card for one of your puters. From the router, have one puter and the ps2 wired in, and the other puter on the wireless card. Linksys is rather easty to set up and is not that much

I could rant and rave all day about networks but I won't

I am not sure I explained this right so if ya have a question, just ask
