Most partner dances involve contact to some degree. Maybe some old folk dances, or some more formal dance from a more restrictive era. Tango, tagor, ergo sum - no, not the origin of 'tango', just Latin for "I touch, I am touched, so I am". Most people desire touch to a degree, but then we all have our personal space, which varies between cultures.if that kind of contact is ok, the swing dancers might work
If 'touch' is a problem, then you'd have to be highly selective about dances. Social Argentine Tango is just intimate.

