UV penetrates clouds, but probably not the watch glass cover. The watch solar charger uses less energetic visible light; it will charge it up under an indoor light bulb. So it really won't work as a good proxy for UV solar exposure.
I use this EPA site:
Link to Seattle version
Here, it is easiest just to avoid peak UV (between 11 am and 3 pm) if possible. I use long-sleeve jerseys and other physical blocks whenever possible.
I think the points people have raised about the variability of wrist position and angle with respect to incident sunlight are valid concerns. It might work better if the watch was on one of those handlebar mounts, but it probably would be more useful as an indication of total solar exposure.
The problem with photons is that there is no safe limit for exposure. One single UV photon is enough to dimerize two adjacent Thymines in your DNA, and if it hits the right ones, could cause a cancer-inducing mutation. So increased flux/lux/whatever is simply increasing the
probability of a transforming event. There is no safe threshold below which you don't have to worry.
I always wear bike gloves, but had a skin cancer on my hand removed 10 years ago.