Probably better to ask Motability, explain your injuries and concerns and see what they can come up with?
Your car may officially be due in January, but it may take longer to arrive, your medical problems may be resolved by then.
If your car does arrive before you heal, see if you can get a friend on the motability insurance and ask if they could take your old car to the dealer and take away the new one. You would of course have to be there to sign off the pin etc.
But motability will have dealt with similar problems to yours and will have a solution.