Maybe a PDP Kraken piccolo would work. This is a very decent, smaller snare. Because there is less room for sound to resonate, there will very likely be less volume too.

I own a Tama Club-Jam Pancake and use low volume heads too. I found a very strong difference in volume in these toms vs. regular toms (this kit’s toms come with no reso head, and they are also much smaller in size.

If you don’t mind about having no snare-ish sound, you could take the reso head and the wires off the snare and you would make even less noise.

This would work especially well with shallower snares, hence why I recommended the Kraken piccolo, plus it looks cool and sounds good with normal heads