Another commonly-used word for a prostitute is hooker. Although a popular etymology connects "hooker" with Joseph Hooker, a Union general in the American Civil War, the word more likely comes from the concentration of prostitutes around the shipyards and ferry terminal of the Corlear's Hook area of Manhattan in the 1820s, who came to be referred to as "hookers".
I think whether or not someone thinks a word is derogatory depends on the POV. Some words, are, in and of themselves, derogatory. The N word comes to mind, even though some people use it with impunity.
There are derogatory words used in relation to other races and/or persons with certain national origins.
But, as far as occupations are concerned, it's a little harder. We could argue, but I think whether or not an occupation's description is derogatory depends entirely on a person's POV. For instance, for some, a "cop" will always be seen as a "pig" or the enemy. While for others, they will always be seen as people who serve and protect.
So, if you are a lady who is OK with the term "hooker" that's all that counts. If you're not OK with it, that counts as much or more.
Me, I try to use the term "ladies" on this board and try to stay away from terms like "hookers," "providers," "whores," etc.