If the watch really reads 3.45 microsievert/hour on the case back, then wearing that watch 12 hours every day gives your wrist an annual dose of 1.5 rem (= 15 mSv), which is not neglible (15 times cosmic radiation background), and roughly in the range of a CT scan. I would not wear that watch more than 10% of the year, and I am a radiation worker. Assuming of course your meter reads correctly.
Regarding the Radon, to be completely safe, maybe venting the safe to the outside could be done? But I wouldn't be too worried if you can't; you are diluting the activity in the safe by a factor ≥5000 (assuming the safe is 0.2 by 0.2 by 0.2 m, and the room 15m^2 by 2.5m high), so that brings the 500 Becquerel down to a safe level. Maybe avoid taking a deep breath right from the safe after you open it.
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