The thing about entering massage parlors/saunas as a tourist…

No, not at all.

Most of the prostitution is gang controlled, that is true, but it is not unsafe for customers except in the lowest end of the business.

Saunas and Massage parlors are perfectly safe. Most houses ("Depas") with girls to choose are perfectly safe and all brothels, within the brothel's premises are perfectly safe.

Of course brothels are not located in residential areas so the surroundings might be a little less safe but if you don't stroll around the neighborhood alone, just get there and back in a taxi, they are perfectly safe.

A wingman would be useful to help avoid pickpockets but not an absolute necesity

 

Very unlikely. In fact, you won't be asked for your ID at a sauna or at a depa, or at a brothel, unless you look like a 13 year old.
At a hotel, however, even at the cheapest hotel, you will be asked for your ID. Most low end P-4-P hotels won't ask you to register, but will keep your ID at the front desk and return it when you leave. Middle range hotels will ask you to register and keep the girl's ID at the front desk. High end hotels will probably register the girl too.
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