Wrestlers herpes is called herpes gladitorium, or mat herpes - https://www.healthline.com/health/herpes-gladiatorum Because the contact they have with each other is rough, and involves a lot of friction, if someone has a cold sore, they can transmit it. Mat herpes is hsv1, not hsv2.
Yes, avoiding genital to genital contact is a good rule, as some STDs can be transmitted by genital to genital rubbing and grinding, like hsv2, HPV and syphilis. This can happen even if you use a condom.
There are other things to be concerned about than STDs. MRSA is always a concern - that's an antibiotic-resistant staph infection. Make sure they disinfect everything between clients, and the entire facility is very clean. If they use oils, make sure they aren't re-using it.
It's also cold and flu season. If the person appears ill, reschedule.
Welll for sure no genital to gental contact. And remember that it is shown that professional wrestlers to contract herpes from body contact sometimes.