If things are as you say, I guess your stuck with shutting off the
water supply, cutting the valves off of the water supply pipes, and
then reinstalling standard shut-off valves. You might have to couple
a short piece of pipe on, and then put standard supply valves on. I
assume these valves are glued on to plastic pipes or they're soldered
on to copper pipes?
Either way, just add some pipe and caps so that things stick out of
the wall, then cut nice holes in the new cabinet, then cut the caps
off and put the valves on.