Disable a wireless module RF
Your dermatitis is not caused by the WiFi. The radiated power emitted by these devices is far too low to cause physiological effects. The most discomfort these electronics would cause would likely be due to thermal effects.

Instead, look for other sources of your rash. Certain metals may cause an allergic reaction in some people; nickel and chromium are common sources of problems. There are some plastics that also cause rashes in some people (Fitbit learned this with their first release of their Flex tracker; more recently McDonald's recalled a bunch of plastic toys for the same reason.)  Reactions to plastics are sometimes due to outgassing, so it might not even have to make direct skin contact to cause the rash.

It's also possible your device's finish is harboring bacteria or fungus, which remain alive in tiny pores in the surface, living off of your sweat and dead skin cells. These could re-infect you every time you play.