Speaking of cats...

If you enjoy non-sexual touching, get a cat. Cats are wonderful for that. Then you can set of a division of labor within the household: your H would be responsible solely for sexual touching and you cat(s), for non-sexual. Sometimes making your family members accountable for a narrow set of responsibilities works quite well.

Dogs also might work well for non-sexual touching, but dogs are a handful, need to be. Walked, etc.