All my hams have come out of their cages on their own terms, two of them were years and years ago before I knew anything about hamster care really, but I've always stuck by never making them come out when they don't want to. I personally use an exercise ball, I know some people don't, but they know ball means out time and they can say no if they want to. I don't like lifting hams who don't want to be lifted, I've tried and it's set me back. Getting to that stage is great for regular health checks and personally that's p much the only reason I feel it's necessary unless they're about to put themselves somewhere dangerous.
I would let them come you you, taming should always be on their terms and by their pace. Lifting a teeny tiny prey animal is a huge step for them and you should try not to be disheartened if they aren't okay with it. Just take it slow
