Gut reaction: don't worry about it. I am not an expert.

Way you can resolve this intellectual puzzle you (had) created for yourself:" How much UV light is reaching the "medieval tapestries"?

Fortunately, this is a problem that has been solved many, many times before. Unfortunately, you need to do math. I plugged "light intensity calculator" into google and came up with this: https://sciencing.com/calculate-light-intensity-7240676.html.

Note: when you do your calculations you need to calculate the UV led power, not total power of the light. To figure that out you'll need to use the light specs. They will list the number of UV diodes and there will be a listing of how much power each diode uses (take the average if it's not listed). This is the wattage you put into the light intensity calculation (I'm sure someone has made a calculator on the internet you can plug the numbers into).

If you want just a superficial argument? Unless it's a super high power UV light, by the time it crosses any significant distance it won't have any 'effect' because it has scattered so much. Especially if it's getting indirect light. The UV portion is quite small of the total power. It might be 1/100th the power of sunlight if not lower (do the math if you care).