The advantage of 622mm rims is the much larger range of tyres available. 630mm wheels seem to have one or two available where modern road wheels have dozens if not hundreds of options.
Another thought is your rim – the 630mm rim is likely to be made of chromed steel. Aluminium rims were not at all common then, and the braking performance of small pads on steel was poor normally tending to non-existent in the wet.
If you want a period-correct bike, 630mm is your answer. If you want a bike to ride, 622 is a better answer.
The only downside is brake reach. A 622mm rim is 4mm lower, so your brake blocks have to slide down 4mm, which may be easy or may require new calipers, or a modification to the hanger bolt. New longer-reach calipers may not work as well with your existing brake levers, so there are gotchas.
Or – no one can spot the difference in size. There is no problem riding wheels of different size, other than you knowing they're different. Even your spare tube should fit both wheels well-enough.
As for the hub, it's not dependent on the rim at all. You can run a 7 speed cassette on any freehub that has matching splines. All you need to do is add enough spacers before the cassette goes on, so that the final lockring has good thread engagement onto the freehub.
I've put a 7 speed cassette onto a 10 speed freehub body as a test, and while it needed ~3 spacers, it fitted fine. As an added bonus, if the chain jumped the cassette for some reason there was less chance of the chain munching the lower spokes because of the extra space.
Your gotcha here is the OLD, or Over-Locknut Dimension. A 7 speed rear wheel was probably 126mm from side to side, and a higher-speeds wheel is probably built on a 130mm or 135mm OLD axle standard.
It is possible to "cold set" a steel framed bike and then align the dropouts to be parallel, but there's no going backward to the older 126mm standard.
Your mechanic's idea of replacing the rim on the existing 7 speed hub is workable too, but will require a complete wheel rebuild, and probably needs different spokes. The new rim MUST have the same spoke count as the hub, which is probably 32 but might be 36. Other values are possible too. And most modern rims are a bit "deeper" and look different. Finding a modern "box section" rim that isn't at the budget end of the scale may be challenging.
You could be sneaky and use a modern wheel, and then wrap the spokes to form a disk wheel and hide the modern rim, but disk wheels are uncommon on the road for a good reason – they're awful to ride in any cross wind or when a large vehicle passes. Plus it would be hard to match the Period-correct look.
