Sonic Blast Man:
SNES (1992, published by Taito)
1 player
https://www.gamefaqs.com/snes/588671-sonic-blast-man/faqs/74893
The "Screw Bomb" also drains health if it connects.
Sonic Blast Man II:
SNES (1994, published by Taito)
1-2 players
https://www.gamefaqs.com/snes/588672-sonic-blast-man-ii/faqs/74924
Legend transcribed to the gamepads buttons:
LA = Y
HA = X
J = B
R = A
Much better game than it's predecessor, more than 1 character, 2 player mode(which runs smoother than the 2p mode in the Final Fight series), just an all around enhanced sequel.
These are the kind of games that are nothing at all like the arcade games with the same name. The arcade games are the type where you punch a board to make stuff happen on screen, so in a way they still requires melee action, but they aren't beat 'em ups.