I was thinking about buying a modded N64 where it is region unlocked. Would this be allowed or do I need to buy a Japanese N64?

Yes, it's allowed. Both the US and J consoles run at the same frame rate. I'd honestly recommend your N64 be region modded, especially if you're talking about buying a modded US N64. It is possible to have a special modded PAL N64 that can run at an NTSC frame rate. However, that mod is obscure and expensive, and I'm not even sure if the that mod causes PAL to run at the exact NTSC frame rate. If you're talking about that specific mod, then I'm not sure if your console would be allowed.

You can play Japanese games on a US N64 if you can get a hold of one of the screwdrivers that can open the cartridges, then take the back off of a cheap US cart and put it onto the back of the Japanese cart. No other modding required.

Replacing the shell is certainly one way, an alternative is removing the tabs in the n64 itself. Though I couldn't imagine harming a poor innocent n64, so I just bought a JP one too.