This actually happened in my hometown. The women were charged and the parlor shut down. You do NOT need a license to be a "body rub practitioner", but the catch is you cannot advertise as a massage therapist, because you didn't do the schooling. But you do need a business license and a legit front, be it "one person there has the actual massage therapist license", or "this is a spa and we do nails and we have nail tech licenses", or "this is an alternative health center where we do reiki" or whatever. There's all kinds of fun code to find out if the place you showed up at does "those" massages.
The man was not charged, as it was his word against hers, and yeah, she had video footage to threaten him with, but apparently that trumped him seeking sexual services. I do believe this was the correct decision. Blackmailing is really the crime in question here, with the laws existing as they do in my province.
Here, prostitution is "decriminalized" to some extent, so she would not be arrested for offering sexual services for sale; if she were not blackmailing him she would have been fine. However, there have been several men arrested for soliciting prostitutes for sex. Had she NOT been blackmailing him, he could have been arrested for seeking these services. Likely not, but consent doesn't matter, as it is illegal here to purchase sexual services.
Uh well in real life? No. You should not kill someone. Murder is not a good solution. Do not kill a masseuse who's trying to blackmail you. In story life? Do you want this character to be a "kills someone in response to panic" type of person? It will make him seem like a bad guy too, if you're going for an "everyone is gray" story, then why not. If you want him to be like panicking rich guy who just wants it to go away? Pay her off. If you want him to be fully lawful good, he apologizes to his wife profusely and then goes to the police. You're the writer, you know what you want this story to be driving towards.
His decision is critical in showing what HIS moral character is. A good person may solicit sex, and if you want him to come across as a good guy who made a horrible mistake, or a neutral guy who's trying to shove it under the rug, going to the police or paying her off is the right choice. If you want him to be perceived as dangerous or frightening, killing her or somehow twisting the situation so he has the upper hand is the way to go. You don't need to kill your masseuse, just frighten her enough to shut her up. Or get the phone.
If she is an actual massage therapist, I can tell you she 100% knows better, and any legit massage therapist looks down on "masseuses" and would never risk being lumped in with them. I've only encountered actual RMTs who have nothing but contempt for "sexy masseuses", and so I have trouble believing that a registered massage therapist would take this action. She will lose her license and any professional respect. She'll probably be limited to working in the rub-and-tug joints. I do believe that someone who gives good massages, who's not registered, may have a client who doesn't realize she's not registered... who may believe he's coming to a perfectly regular establishment... maybe he enjoys the low price for the basic full body massage (because someone coming in for extras would be tipping significantly above that in cash).