While this sounds likely to be the correct answer, the first thing I thought when I glanced at the question was Cerberus: A Wolf in the Fold, by Jack L. Chalker. This is book 2 of the Four Lords of the Diamond series by Chalker.
Background: a human interstellar (possibly intergalactic) empire located a system with four planets, called the Warden Diamond. The planets cause humans who go there to be unable to leave the system, and to develop various mental abilities. The system is used as a penal colony; however, aliens are reaching out to the inhabitants of the system, and are fomenting unrest.
An agent is sent in to track down the leaders of the four worlds who were dealing with the aliens, and regain control of the situation. Humans have a sort of "body swap" technology - they can basically record the mind of one person, and use that to overwrite another person's mind; the other person becomes a mental copy of the first (the other person's own mind, however, is gone). So, four mental copies of our agent are sent out, one to each of the four worlds.
On Cerberus, the ability humans gain is the ability to swap bodies (without a technological crutch, and with both minds actually swapping bodies, rather than an "overwrite" scenario) with others from that same world, which happens while the two individuals are asleep.
I'm pretty sure there was some way to prove your actual identity (a necessity from a logical standpoint, after all), but I'm not sure what it was off the top of my head; it could have been ID bracelets, but I think it was more automatic than that (note that this was basically a planet full of white-collar criminals).
The agent's "mental copy" in this book is female (the lead character is male); the copied agent makes sure to fall asleep next to a man on the first night, and uses that as his primary body for the start of the book (technically "bolting" with it).
The central conflict is the between the galactic government, the aliens, and the leaders of the four worlds in the system.
So, the same central conceit, and several matching/close details. However, there are notable deviations from the work described by the OP:
- The body swap doesn't happen during sex (although, if the partners then fall asleep in close proximity, it would happen).
- I have no recollection of anything regarding belly dancers.
- Since the swap took time and sleep, there would be no benefit in swapping deliberately to continue meetings or anything; a meeting would have to be interrupted for hours, after all. Thus, there was no market for bodies to borrows, as appears to be the case in the desired book.