Alright, this is a dangerous process, and
absolutely not recommended by anyone, so try it out at your own peril.
(The experts are gonna kill me for mentioning this. *sigh*)Firstly, get a .pk3 editing software such as SLADE and install it.
Next step, and this is most important part of it, is to make a copy of MM8BDM-v5c.pk3(current version as of this post) in a separate folder. This is your backup file in case all goes wrong.
See, how this workaround works is that although you cannot play online with modified files due compatibility issues, there are exceptions to this such as sprites and HUD.
Anyway, next, you open SLADE, and there, open the MM8BDM pk3 located in your MM8BDM folder.
In your case, it's just some music, so in the contents of your MM8BDM pk3, find musics.wad then export it.
Open your newly exported musics.wad and replace what you'd like to replace. Replace the musics.wad in your MM8BDM pk3 with your own modified version, then save.
If you do not prefer the above method, these other methods are a thing, but come with their own downfalls:
*You can load your file as an additional file in the MM8BDM launcher, but this is best used for offline play, which while it's fun in its own right, just doesn't hold up to proper multiplayer.
*If you'd like to use your custom replacement content online without the above risky method, you can always host a server with your custom file as one of the additional files(after MM8BDM's core of course). Unfortunately, this is undesirable among some players who'd like to join. You can always make it an optional file, though.