Ship of Harkanian, the PC port of OoT created from the decompilation project, has the randomizer built in. It's the best way and probably easiest on PC.

You can also build an actual N64 rom and play in an emulator or on a real N64 using a flashcart. RetroArch N64 cores will work fine with it.

If you're just playing it for fun the PC port has randomizer seed support as well as a ton of other QoL improvements. If you're doing things as part of a group race there might be a requirement to use only certain emulators or real hardware though, depending how much the group cares.

In general, if you can play the game on the system you can probably get the randomized ROM to play on it.

It should do, it can run on original hardware (e.g. via an Everdrive). I play on a MiSTer FPGA [0] and it's great.

[0]: https://en.m.wikipedia.org/wiki/MiSTer

I use OpenEmu on my Mac, so I guess Mupen64 as the emulator core. However as someone else mentioned the ROM should run on native hardware.