Comment by mrob

Only the oldest CRTs used leaded glass for the front, because leaded glass gradually turns brown on exposure to X-rays. More modern CRTs used glass with barium and strontium for X-ray shielding in the front. They still used leaded glass for the back and sides, presumably as a cost saving. I don't see any reason why you couldn't use the barium-strontium glass for the whole thing. Alternatively, CRTs could be made with ceramic bodies like Tektronix used to do.

The energy of the X-rays produced is limited by the CRT's acceleration voltage. The electrons get almost all of their energy from the field produced by the acceleration voltage. Electrons can produce photons when they hit matter, and one electron produces at most one photon, so by conservation of energy the X-ray cannot have greater energy. Smaller CRTs typically use low acceleration voltages, which means the X-rays are low energy and thus easy to block.