My setup involved testing three tubes in my collection used from time to time for testing arcade pcbs, retro consoles, as well as micro computers. I believe these models are also commonly found among the gaming community and they should be somehow representative.
In front of each tube an X-ray sensor is placed at different distances: 3cm, 30cm, 60cm. X-ray activity is sampled during 180 seconds during each run, then compared against ambient readings (tube turned off).
Initially the X-ray sensor is left to warm up for a good 10 minutes to obtain constant ambient reads.
|Toshiba A68 CRT (NANAO MS9) on a New Astro City cab|
I'm afraid to break the news but... there's no such thing as a free tan while retro gaming. At no time any of the tubes tested presented any abnormal sensor reads indicating the presence of X-rays. To put things into perspective I have included a table below comparing the different scenarios together with reads of the sensor exposed to radiation from a controlled x-ray source.
I'm no expert on this matter, but even if the energies inside the tube are high enough to produce X-rays, the glass in your CRT has lead in it to block those from reaching you. Perhaps someone with enough expertise could confirm these assumptions.
Happy safe gaming.