Sure, the titles for a hooker main character could be funny:
The Trick to Murder
Dear Dead John
Hooked on Death
Unfortunately, cozy mysteries, while dealing with loss of life, are not about the dark underbelly of the world. A prostitute's life is inherently more dangerous than the life of a maid/barista/beloved pet. Contrary to what Pretty Woman would have you believe, there is very rarely a happy ending in marriage to a billionaire. The cozy mystery is about fireside reading, not I'm-never-going-outside-in-the-dark-again reading.
The jobs that occur in a cozy mystery are all of the 'everyday' variety. The whole point is that these main characters are intuitive and have some kind of observational advantage because of their job. It's also convenient because it automatically lends a lightness to the work that wouldn't be in there in a traditional P.I. or detective story.
Hopefully, if executed well, the characters are also that much more likeable because they don't have lab techs getting them fingerprints, or gun-toting partners to back them up, or any kind of real authority when it comes to facing down the bad guy. Everything is through logic, observation, and ingenuity. The puzzle pieces should be presented in such a way that the other jes'-folks detective (the reader) can put it together with the main character.
A butcher, a baker, or a candlestick maker should be able to read a cozy mystery and not feel like they are being assaulted with the darkness of the world. So, when choosing who will tell the story, just keep in mind that your fourth grade teacher should be able to relate to the main character.