You actually could probably crazy glue it and it would likely be ok. The screen actually holds in place pretty well without the screws so a big of crazy glue would probably work - crazy as it sounds. But I thought that the connectors on the back of the display were slightly different too... like the little micro connector for the front camera... I thought that that connector was slightly different...? But I'm not sure. I have repaired one 4S and one 4 and I wasn't paying that much attention since they were months apart.
You could try and see how it goes. But if you aren't totally hard up for cash, my advice matches bearxor's... I'd just get a cheap screen on Ebay.