Virtua Fighter & Virtua Fighter 2 MUSIC TRACKS apparently has a breakdown that covers most of the tracks here (source is ultimately
this page).
Takayuki Nakamura & Takenobu Mitsuyoshi: 1, 4, 7~10, 16
Takayuki Nakamura: 2, 3, 13, 22, 23
Akiko Hashimoto: 5, 6
Takenobu Mitsuyoshi: 11, 14, 15
Takayuki Nakamura, Takenobu Mitsuyoshi, Akiko Hashimoto: 12
??: 17~21
JASRAC agrees with all of this and gives track 18 to Nakamura too. 17 & 19~21 are credited to all three, which I think here means "we don't know who did it so we're crediting everyone" instead of "all three people composed this ten second jingle."