Might be too thin to press properly, and the hard plastic might still rub against the shell.
As for the membranes, they may not mount properly since the GCW has 4 mounting posts instead of the Vita's 3, and I don't know how well they match up.
Don't think it's worth the risk (damaging wires inside the GCW) or effort when you can buy 3d printed ones designed for the GCW.
Silicone grease is also a valid low-cost option, which I used up until I bought 3d printed buttons.