xdelta requires you to have an input ROM matching the one it expects as it is not as much a list of changes as a quasi compression scheme that might reference other things and relocate data. Some things will allow you to force it to attempt it on a non matching file but I don't know if the later versions (which I believe this uses) will.
Looking at the releases (
http://advanscene.com/html/Releases/dbdswrel.php ) though then there is a "pure" version which claims the Scene release (which the patch most likely expects) has a bad header. 99% of the time this is the aggravation of pointless redumps. Short version is for most of the DS history a section of the header went unused, however upon the release of the DSi all ROMs past that point used said previously blank area to house a signature (
https://hackmii.com/2010/02/lawsuit-coming-in-3-2-1/ ), the main dumpers of the time (Rudolph's in most cases) carried on ignoring it but later ones (whatever DSi/3ds ones and wood dumper,
https://www.gamebrew.org/wiki/Wood_Dumper ) do not. Said extra data is of no value to basically anybody -- no emulator cares, no flash cart cares, no ROM hacker cares, no game player cares but we do now have the split to contend with and the only time anything in the future will use it is if they make a pointlessly accurate DSi or 3ds emulator or hardware recreation.
You can try blanking out the area, though I am not sure which it is offhand. I should really do a test actually as it would be an identical patch for every game (fixed location and going to blank after all). Or you can find whichever of the The_Legend_of_Zelda_Spirit_Tracks_USA_READNFO_NDS-XPA or The_Legend_of_Zelda_Spirit_Tracks_USA_PROPER_NDS-NoGroup releases it is and go with that.
Other occasions may see either a fixed version released to sort a bug or censor something (
https://www.zeldadungeon.net/wiki/Ocarina_of_Time_Versions is not this but illustrative) which obviously changes something but I don't think that is the case here (said releases do have a v01 but that looks to be a demo version).