Reading a do-it-yourself guide to PEX (link), it looks like running PEX isn't all that much worse than running Ethernet wires. You have to leave enough slack for expansion, and you have to make sure the weight is properly supported, but none of that sounds too rough. You'd definitely want somebody to show you how to do the crimps properly. I'm guessing you'll have a much harder time opening the walls to get at the old pipes than you'd have installing the PEX to replace them.

Somehow, I imagine you end up leaving the old copper alone rather than trying to hack it out of the walls. Still, the scrap value is somewhere in the neighborhood of $3/pound, if I'm reading this web site correctly.