Resting the camera and using the self timer can work well; well enough that you don't have to necessarily jack up your pics with ISO settings that may end up being too noisy.If there is a flat surface that you could set the camera on, then you might try putting down a beanbag (or a folded thick cloth or the like) for the camera to rest on, then use the self timer to actuate the shutter.
Flashes also emit UV. A big no-no in a room full of priceless artifacts.It's not uncommon for public buildings such as museums or galleries to forbid the use of tripods. Flashes too. They interfere with other patron's enjoyment of the facility.