Attending university-sponsored club events as a faculty member?
The short answer is that this really does depend on the strictness of your institution's conduct policies.

However, I would think that in such circumstances—in particular, it's a club where everybody knows physical contact is required—it would be understood that such contact would take place. Therefore, so long as the contact is limited to what is appropriate for dancing, I don't see why there would be an issue. 

(You may also want to look for off-campus swing dancing opportunities—getting away from campus may be helpful for work-life balance.)