I've done both and the mug warmer is more convenient.
With the pot, you can't take your attention off it, you risk the vials falling over (especially once the oil volume is low), and if you label them, the labels will come off unless you have water proof labels or put tape over them. Plus, getting close to boiling is maybe too hot? Not too hot for the oil, but maybe too hot to inject, and definitely too hot to handle immediately.
With the mug warmer I turn it on, put my oil vials on it, then do my peptides and whatever else, then come back and pull the oil.