Check your local statute but it is probably not dissimilar from:
§ 18.2-346. Being a prostitute or prostitution.
A. Any person who, for money or its equivalent, commits adultery, fornication or any act in violation of § 18.2-361, or offers to commit adultery, fornication or any act in violation of § 18.2-361 and thereafter does any substantial act in furtherance thereof, shall be guilty of being a prostitute, or prostitution, which shall be punishable as a Class 1 misdemeanor.
B. Any person who offers money or its equivalent to another for the purpose of engaging in sexual acts as enumerated above and thereafter does any substantial act in furtherance thereof shall be guilty of solicitation of prostitution and shall be guilty of a Class 1 misdemeanor.
(Code 1950, § 18.1-194; 1960, c. 358; 1975, cc. 14, 15; 1980, c. 534; 1993, c. 609.)
§ 18.2-361. Crimes against nature; penalty.
A. If any person carnally knows in any manner any brute animal, or carnally knows any male or female person by the anus or by or with the mouth, or voluntarily submits to such carnal knowledge, he or she shall be guilty of a Class 6 felony, except as provided in subsection B.
B. Any person who performs or causes to be performed cunnilingus, fellatio, anilingus or anal intercourse upon or by his daughter or granddaughter, son or grandson, brother or sister, or father or mother is guilty of a Class 5 felony. However, if a parent or grandparent commits any such act with his child or grandchild and such child or grandchild is at least 13 but less than 18 years of age at the time of the offense, such parent or grandparent is guilty of a Class 3 felony.
C. For the purposes of this section, parent includes step-parent, grandparent includes step-grandparent, child includes step-child and grandchild includes step-grandchild.
(Code 1950, § 18.1-212; 1960, c. 358; 1968, c. 427; 1975, cc. 14, 15; 1977, c. 285; 1981, c. 397; 1993, c. 450; 2005, c. 185.)
Parts of § 18.2-361 would no longer be enforceable, but what the law on prostitution can be summed up as in Virginia is “money or its equivalent for actual fornication or a list of sexual acts is a crime.” Touching that would not meet the definition of any of those sex acts in either of the two statutes would not be seen as something you couldn’t pay for.
So paying someone to cuddle is no more illegal than paying someone to shake your hand.
However, if you are caught up in a prostitution sting then you are almost definitely going to jail the moment you go into the hotel room with the police officer posing as a prostitute. I think it would be very, very, difficult to avoid going to jail and it would be very difficult to not be convicted of the crime.
That being said you probably have less than 1% chance of ending up in such a situation.
Prostitutes themselves are not particularly interested in cuddling though, they have an expectation of a John’s behavior and what you’re asking for would probably be objectionable to some prostitutes. Further, many / most prostitutes are probably not people you would want to cuddle with. They might have open sores, probably smell bad from constant chain smoking, and various other things.