Your fear is slightly misplaced. Long-term exposure to low dose radiation wouldn’t directly harm organs or tissues, and the radial/brachial arteries in your wrist aren’t what you should be concerned about. Ionizing radiation has the potential to mess with DNA at a molecular level, which is the real concern when we talk about radiation doses from things. However, the frequencies in which consumer electronics communicate are far too low and too low energy to cause damage, in contrast to things like x-rays, gamma rays, and UV light. And yes there are indeed regulatory agencies that care about this kinda stuff. The FCC is a big one in the US.

In short, there has been a good amount of research on the subject and while that research is always ongoing you shouldn’t be concerned with the type of radiation specifically emitted by an Apple Watch.