Mismatched rims, and tires that may be too wide? I am currently most of the way through a 1x10 conversion of an old (early 90s) mountain bike. As part of the process, I had to replace the rear hub, and the only one I could find locally came installed on a rim (Equation aluminum, labelled 559x16, measured 16.25mm interior width). The old rims were larger (Araya, labelled 26x1.50, measured 20.25mm interior width). I own two nearly-new (well, 15 years old, but never really ridden) Maxxis tires, labelled 56-559 as well as 26x2.10.
I understand that tire and wheel sizing is a deep, dark hole, but from Sheldon's chart, it looks like these tires are probably too wide even for the wider of my rims, and definitely too wide for the new, narrower rim.
So I'm wondering what my best strategy is:

Just run with the tires and mismatched rims I have, the difference is too little to matter
Run with mismatched rims but replace the tires with either a matched set or two individual tires that match their respective rim
Move the new hub to the old rear wheel and run with the tires I have (noting that I have none of the equipment I'd need to properly build a wheel)
Replace the front wheel with a rim that matches the rear wheel and run with the tires I have
Replace the front wheel and both tires because those tires are way too wide for 16mm rims
Any other novel, clever suggestions you might have
The thing that confuses people about all the newfangled inner rim width to tire width compatibility charts is that while the effect they're trying to steer you away from is real, it's not binary. It gets more squirrelly, floppy, and prone to blowing off the narrower you go. The point where there are major issues in practice depends on rider weight, inflation pressure, riding style, the fit of the tires, and other factors.
A 2.1 on a 16mm inner width rim is somewhat extreme by rational standards, but when rims like that were trendy there were a lot of bikes running around with such a combination. It will probably be fine, but it's on you to decide whether you want the risk, and how reasonable it is depends completely on your application.
Transplanting the hub makes sense as wheelbuilding practice if that's what you want and if the rim and hub in question are in good condition. That kind of job makes little sense from a time/money perspective if all you want is a functional bike, but it's also how skills are built. Use new spokes and nipples.
There are many times when using a rim that narrow creates some hoops to jump through when setting up the brakes on a frame that predates the trendiness of super narrow 26&quot; rims. Eighties and early nineties MTB frames often had rims and post spacing that were about as wide as they should have been. Brake and pad models differ in their ability to get the pads in so far. That in practice is a thing you need to try and see.