Nice open question!
Simple answer is that anywhere you rebuild something (or build a replica) you'll have to have it certified. Each country has different criteria, but someone wants to know you've got an aeroplane with the wings screwed on proper like. In the USA there is the 'Experimental' category, into which fall a lot of unusual aircraft, like W.W.II heavy metal that wouldn't be certified under a more normal set of modern expectations of airplanes. But they are still checked for wing attachment.
To take a couple of real life examples - The Germans got inventive and risk-comfortable at the end of W.W.II for some reason, and designed and built the Messerschmitt Me262, Me163 and the Bachem Ba349 Natter. The 262 engines had a scarilly short TBE (time before explosion) so even a modern build 262 engine is unlikely to get built and used in an airframe. However, the 262 airframe is fine - so there is, today, the first of a batch of replica 262s flying in the USA, powered by a pair of modern American apple-pie J-79 engines.
The Me163 was rocket powered, and quite a nasty little joker as a result. The aerodynamics were interesting. Upshot was that the smart money said we'd never see a 163 fly. Wrong. Some Germans got it together and built a glider version (just like the glider pre-production 163s) and flew it.
Then there's the rocket powered Bachem Natter. I don't think we'll see one of those in the air, as you'd have to be seriously in Goterdamerungungung to see it as any way worthwhile. (But I thought the 163 was a bit mad...)
The clever chaps in Colditz built the famous glider in the roof which never flew. But a replica did, after being checked out by an inspector and lots of care to make sure the wings stayed on (they did, and the IWM Lambeth had it on show in THEIR roof a few years ago!)
In other words, there's few limits to human inginuety, and someone'll look at your aircraft to say if you are alowed to try and fly it. How do they know it'll be OK? You come up with enough paper with enough numbers that are convincing enough. The currency kind you'll have used on the rebuild, so you'll need to provide stress analysis and historical stuff...
HTH