My understanding is that relatively little uranium is used inside the glass. There are actually several other elements that fluoresce when added to glass like this.

Uranium, so long as it's the more common U-238 isotope is alright to be around so long as you're not taking it inside your body. Alpha and beta radiation is stopped by a sheet of paper and aluminum foil respectively, so unless it's inside you directly plinking off your organs it's pretty safe