Swap iphone 4 screens? Possible?

I have an iphone 4 GSM, and just got a relatively new iPhone 4 Verizon.

The verizon iphone is like new but I need to use the GSM iphone because I have a sim card carrier.

Would it be possible to remove the screen from the verizon phone and install it in the gsm iphone? The gsm iphone screen has a few scratches and I hate using it because of this... And then would it be possible to install the gsm iphone screen in the verizon phone?

Let me know thanks!