Part of the trouble of swapping screens is that there are 2 devices in danger of having something go wrong. I have a repair shop and have replaced a Nexus 7 2013 screen before. As mobile screen repairs go, it's a bit easier than average, but that doesn't mean it's particularly easy, and not something I'd advise someone to attempt on a first try unless they have experience working with small parts & attention to detail.
The screen/glass combo itself is a bit under $60. Labor is going to be 30-60 minutes most likely. If you brought it into my shop, I'd probably quote $100 for the repair. Unless you're in SE Idaho, though, the added shipping bumps the total repair cost up a fair bit, so I'm not telling you my pricing to try to sell you on a repair, but to give you an idea of the costs involved. Swapping screens doubles the labor, and increases the liability. If something goes wrong, now there's 2 broken devices instead of 1, and I'd still probably quote $100 for swapping screens vs replacing the screen, due to the increased labor + liability.
So overall, I'd advise shopping around for a shop that can do it for a reasonable price, and just replace the broken screen vs swapping. Then you can sell or use the 16gb to make up for the repair costs.