Nothing stands out when it comes to striptease clubs in Basel. Except for the prices, it is Switzerland after all. Red Rose at Clarastrasse 52 is something I would personally recommend. The floors are dirty, the lights are dim; it just feels like home.
Copacabana (http://www.nightclub-copacabana.ch/) at Untere Rebgasse 3 is another titty bar in Basel I would happily frequent. No one will try to scam you, but remember that prices are so ridiculous that a night out can cost you more than €400.
In and around Basel you can also find some respectable FKK clubs. These German adult versions of a sauna club are usually filled to the brim with sexy independent ladies offering pleasure for payment. Pascha Basel (https://pascha-basel.ch/) at Vogesenstrasse 137 and Club History at Hammerstrasse 24 in the nearby town of Liestal (http://www.club-history.ch/) are both safe picks and swarmed by stunning girls. What I like about the sites of the clubs is that they publish a rooster/timetable of available ladies. So before heading to the club you can already check with whom you would like to get acquainted once you are inside.