I think I would get it checked by a vet if it's floppy in case he's broken anything. They may be able to prescribe some meds too and will advise on whether he needs to be in a hospital cage type set up or not, or whether he can stay in his current cage, or whether you need to make some adjustments.
What cage do you have, because they shouldn't really be able to get a paw stuck in the bars? Even narrow bar spacing is usually big enough for paws.
I had a look at your other thread and his photos
Is it the plastic pets at home cage? Just wondering if it was the door he got his paw trapped in or somewhere else - I do seem to remember there are some gaps between where the ladder meets the shelf in that cage where a paw could get trapped?
Do you have a pet carrier to take him to the vets in? If not then, if the cage isn't too big to carry you could take him in that, if you could have it on your knee on the way there and hold on to it! In case of any sudden stops etc. If the cage is just in the car and it brakes suddenly they can get thrown across the cage, but should be fine if you are holding it on your knee.
Although you probably have a pet carrier as you've had a hammy before