Alpha: In the hand held away from the body would be reasonably safe. In a pocket of a lab coat might provide a little more shielding from the body with the coat material, but it is physically closer. Eaten would be very bad for the user, but protect the outside world the best

Beta: Medium penetration, would likely not be safe in any of these three situations

Gamma: High penetration, definitely not safe in any of these situations, best would be to get it as far away from you as possible, so held at arms length would mean you might only get high radiation exposure in your hand. Hospital visit is probably needed in any of these three situations

It absolutely is the point though? You can't rely on the LLM to not tell itself to do things, since this is showing it absolutely can reason itself into doing dangerous things. If you don't want it to be able to do dangerous things, you need to lock it down to the point that it can't, not just hope it won't