I have played games of FIDE Chess with W giving odds of all 8 Pawns....
With both sides no Pawns, I'd try 1. Qxd8+ followed by 2. Rh1xh8, which
ought to win.
With Pawns replaced by W or F or Berolina Pawns, in a sense it's not so
Pawnless, is it?
Racing Kings is Pawnless. It has a different goal, and perhaps you could
argue that it's not even Chess. However, in the process of becoming NOST
postal champion a few years in a row, I learned to appreciate what a great
game it is.
Without using really weak pieces to replace Pawns, you could probably find
a setup on the 4x16 circular chessboard that works.