You sound like you have read a few things but anyhow
The most common DS sound format is SDAT, it contains 3 sound types
SSEQ - this is the midi like sounds.
SWAV - usually packed inside SWAR files. These are the audio samples and the like that are used for short sound effects.
STRM - this is longer audio tracks, they are quite rare though and have been known to exist outside the SDAT file.
There are minor variations/containers and music banks for the SSEQ. Trouble is most things that play with the SDAT audio container on the DS do sound effects as well and they very much play second fiddle to SSEQ. Some of the earlier sound tools do a better line in ripping the audio and not converting it but ndssndext is likely the best audio tool we have for the DS (newer versions of VGMtrans are not bad though but not what you want here).
Other sound formats exist but they are very simple compared (usually a more elaborate form of wave file you can treat like any other simple file).
This being said you seem like you do not want the SFX files for easy playback but as a way to merge them back into a sound file and have the rom use it.
Easiest way to lose background music is to point all the SSEQ files (the midi style audio you might hear) way outside the sound file- you might have seen the tetrisDS sound hack that did it, one was done for pokemon if memory serves (if not it was exactly the same technique) and the early Castlevania portrait of ruin stability hacks did the same thing)- general idea
http://gbatemp.net/index.php?showtopic=122534 except where the locations were changed to other files stick it way outside the SDAT file.