It would be wonderful if we knew that. It would be wonderful if we had any solid facts and figures from any of these countries, but we don't; there are only the vaguest guesses as to how many sex workers of any kind there are, and only anecdotal evidence for whether they are happy with their work or not. A large part of the trouble with this debate is that it is mostly built on guesses, information supplied by very unreliable sources (such as the police) and pure prejudice dressed up as fact.
For example, the anti-prostitution lobby in this country constantly repeats a figure for the number of trafficked women here: when investigated, this turns out to be based on a police guess of the number in one British city, a guess based on the number of arrests over a few days, multiplied up to the whole country. They might as well make it up and be done with it.
Anyone going round brothels with a survey clipboard would be in almost equal danger from the lawless and the law, so it's not likely to get any better.