Here's what I was able to find:
Yoshino Aoki (BOTW Main Theme): Mega Man series and FF15
Yoko Shimomura (Vega Stage from SF): Mario and Luigi, Mario RPG and Xenoblade 1
Yasushi Asada (Brinstar Depths): Castlevania Judgement
Tomoya Othani (Bomb Rush Blush): Sonic series
Maki Kirioka (Noisy Notebok (Snipperclips)): Metal Gear Solid series
Noriuki Iwadare (City Trial (Kirby Air Ride)): Kid Icarus Uprising
Jun Senoue (Mega Man 4 Medley): Sonic series
Nobuko Toda (Snake Eater): Metal Gear Solid series
Takenobu Mitsuyoshi (F-ZERO Medley): A couple of Sonic games, but works for Sega
Yusuke Takahama (Galaga Medley): No Franchise, but worked on multiple songs for Brawl and Smash 4, so Smash*?
ACE (Gang-Plank Galleon): Xenoblade 1 (and 2)
Hiroki Mori****a (Gear Up For… (Fire Emblem Heroes)): Fire Emblem, Paper Mario, Game & Wario (with a BIG emphasis on Fire Emblem))
Shota Kageyama (Yoshi’s Island Main Theme): Pokemon series
Akihiro Honda (Fortess Boss (Super Mario Bros 3): Metal Gear Solid Series
(*Keep in mind that there are other composers besides Takahama that worked on previous Smash games.)
What I've observed about this is that the rule of thumb is to bring composers who are famous from Smash franchises or past games, so if Kaufman is in it, some of his work is more than likely to come with him, remixed or not.
Another question that could be asked...
For the sake of argument, let's assume Kaufman is under an NDA.
If it would be for Shovel Knight music and not Shantae music...
Where would that music play in the game?
Since I doubt Shovel Knight has his own stage....
Probably in the miscellaneous stages, like Wrecking Crew and Hanenbow, considering how songs are sorted by franchise.