According to a friend who’s a former sex worker, meeting with a guy who doesn’t actually want sex (or anything kinky in its place) isn’t that rare, though it often happened with men they’d seen multiple times. Not all women can play the game, though. I imagine having a bad actor pretend to like snuggling is just as bad as them pretending to enjoy intercourse, if not worse. Also, some sex workers, especially street prostitutes, will likely see this as a waste of time (since you’re not going to ‘finish’ quickly).
Third the suggestion of a massage. There’s a reason people don’t all just spring for massage chairs.
I’ve little specific advice to offer, but the phrasing of your question (“Is it illegal?”) raises a big question mark in my mind. Was this just a sideways way to phrase your question, or are you actually worried about being arrested (or embarrassed somehow by law enforcement)? If arrest is your worry, I’d suggest that tendency for excessive caution might be part of your problem.
I was under the impression that cash was legal tender for all debts public and private; heck, it even says so right on the bills. You pay your debts however you like; the burden of reporting the income (and paying the tax on it) is up to the recipient.
If paying in cash is illegal, then when I was a kid my neighbor was breaking the law every time he handed me a $20 bill for cutting his grass (and no, I never did report the income :D).
In prostitution busts I’ve seen one TV (in which either the customer or the prostitute is an undercover officer), the miscreant is required to confirm that the money is being exchanged for specific sexual acts. If you’re giving a woman money specifically to do something other than sex (e.g. backrubs, cuddling, hugging), there’s nothing to bust you for.