Some triathlon gear comes without chamois or with very minimal chamois.
Zoot or
DeSoto maybe. Maybe give
All3Sports a call and ask if they have something.
My Zoot shorts with very thin padding were very comfortable. I wore them on the bike until threadbare and still use them as compression shorts under running shorts for trail runs.
I have ridden in
Tyr "Jammers", made for swimming but who's to know?
-Tim-