But I think that's the better battle music.

Probably the (relatively) easiest way would be to find the pointers to the music data and switch them.
However, I don't know how you'd do that unless you can figure where the music data is.

Yes, it's possible. You'll probably need to trace some code during the song loading to see where it's coming from. I agree with KingMike for the easiest likely approach. You'll have to figure out a bit about the sound communication protocol the game uses to load it's songs to figure out where it comes from. If you don't know assembly, you probably can't do this.

You read. Then you read some more. Read about the SNES hardware from documents on this site pertaining to SPC700 communication. Read about assembly language in Google, read about CPUs and registers. Get a debugger such as Geiger's SNES9x debugger from our Utilities section. Experiment with it yourself.

In between all that, you come back here and ask some specific questions about what you read and what you've tried to yourself. Repeat the procedure over and over, added new reading material and experimenting in different ways. Then you'll start to understand what you need to do yourself and realize why I can't explain to you exactly how to do this. You won't understand the answer given.