Different mod methods have different patch methods (patching is like documents or image formats in that there are hundreds).
If I had an idea of what patch it was I might be able to suggest something.
Wii patching however tends to involve you pulling apart the game (everything from wii scrubber to WIT, the latter definitely having a Linux version
https://wit.wiimm.de/ ) and then patching files using one of a variety of methods (I saw IPS twisted to it, xdelta in various guises, bsdiff, ups and seemingly PPF made a rise from the dead) as the whole discs are encrypted normally, and some people use different formats anyway. Some do further things like chain load them with mods to theoretically allow unmodded machines to work with them, or force people to own the discs but I don't think it is the case here.
I would say however patching done right is the smallest files you can download. If there is a library, internet cafe, friend or some such with decent internet it would be better.
main.dol is the main executable (as in what the code comes in, though not necessarily composed entirely of code as devs have been shown to include all manner of non code data like text, graphics, music, levels in other things at least) is for a lot of wii stuff. Based on the elf format it goes back to the gamecube at least.
"Just Dance mod that brings back world dance floor"
I have no idea what that means (I think I technically own the games but that is more because I got them in a bundle, certainly have not pulled them apart to hack). Is it a background graphics thing, gameplay mode or something else?
Graphics if dragged from an earlier entry in the franchise is potentially tricky (especially as if that is the first Wii game we are possibly looking at PS2 and a graphics conversion), if it is a gameplay mode then chances are it is some more extensive code alteration as by the time of the wii then everything was compiled so old code tended not to be left in to be reactivated.
ARM assembly on the Wii is mostly for custom IOS modules. The games themselves tend to be a slightly older form of powerpc (the wii being something of an overclocked gamecube). If you are reinventing a bunch of code then you will probably have to be doing this.