Most people indulge in erotic massage in Basel when visiting a local brothel, often referred to as sex studio or salon. There are, however, a few spots if you’re not into full service. Azamour (https://www.azamourbeauty.org/) at Gundeldingerstrasse 311 specializes in massage and minor cosmetic stuff like hair removal.
If tiny hands and Asian expertise is more down your alley then Thai Massage Palace (https://thaimassagepalace.ch/) at Dorfstrasse 121, is the place to go. An hour will set you down around €80, which is incredible cheap according to Swiss standards.