My impression from DS9 is not that they are bounty hunters, but that they are isolationists, and are probably zenophobic. The Breen government allies with the Dominion because they see some benefit for themselves. I don’t think it’s a guns-for-hire situation. It seems like the Dominion is quite good at using enticements and threats to cajole self-serving governments that otherwise wouldn’t get involved in quadrant power struggles.

The masks do bear a resemblance to Star Wars bounty hunters. They remind me most of Leia’s bounty hunter disguise. There’s a suggestion that the reason they wear masks and full-body suits is to confuse outsiders. Weyoun says that despite rumors of being extremely cold, Breen actually has a pleasant climate, and so no one knows why they wear refrigeration suits. But since that comes via Weyoun, who knows what’s true.