Many NSBCAs contain more than one animation, which can be viewed using MKDSce. How to swap animations around in those files? I don't think it would be that hard, would it?

It's relatively simple, here's how you do it:
_open the .nsbca in the Hex Editor
_go to offset 0x1D, the byte there (noted N) will give you the number of animations in the .nsbca
_apply this formula (in hex) to find the address where is stored the first animation's offset:
0x30 + [(0xN - 0x1) × 0x4]
or 48+[(N-1)×4] in decimal
_each of the N addresses is 4 bytes long

Just swap the offsets you want and you're set.

I'll try that.

Will this work the same for Mario and Luigi's animations (located in the \player folder)?
I know that M and L's models are similar to NSBMDs but then compressed, but I'm not sure if it's the same thing for M and L's animations and NSBCA files.

I don't see any reason why they wouldn't use the same format as the rest of the models.

True. But the thing is: M and L's models are basically compressed NSBMD files. I don't know if the animation files are compressed. I have to know that before I edit those.

NSBCA inside the "/player" folder indeed need LZ decompression.