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.)

If you are in the US, then it is typical that university clubs have formal elected leadership -- a president, and possibly other officers as well. Generally, they are quite serious about this -- indeed, in graduate school I remember a conversation with a foreign student who joined the ping pong club, and was struck by how earnest the officers were about fulfilling their roles.

I think the club president would be a good person to whom to address your questions; you can probably find out who the president is by Googling, or by seeing if the club has a Facebook page.

Incidentally, I went to university club-sponsored dance events as a graduate student myself, and I remember at least one faculty member who regularly showed up.

I attended a student swing-dance club as a postdoc, and a non-student one where students were present as a lecturer. None of the students I actually taught were present, although there were students who were friends with ones I taught, and they were able to identify me.

I asked my boss about this. The response was that it's ok. However, I did keep an eye out for my students attending. I dance both lead and follow, so if one student had come I would have switched over to avoid dancing with them. If several had started coming, I would have had another think.

As I understand it, for this level of relationship the key point is being aware of any conflict of interest. If you are in a position to affect the academic outcome of someone in the group, someone with more authority than you should be made aware of the situation and respond accordingly, so that everything is seen to be above board.