Hi,
I probably wouldn't wait 10-14 days to remove the piece of stuck shed on his tail if it circles it completely.
Getting it sorted shouldn't be that long an ordeal if you follow the advice in the bad shed sticky.
As long as it has been at least 48 hours since he last ate (or more if your temps were cool as Starmom says ) I would try and remove it - and though the piece on his head matters less you might as well try and remove it at the same time I think.
On the mouse front you could buy a small "critter keeper" and put the mouse in there with some bedding, food and a waterbottle then leave him near the snakes cage for an hour or two without having to worry about him chewing out fo the cardboard or anything.
It is always a good idea to have a cage like that anyway for those times when he doesn't want to eat - you can just keep the mouse till next feeding day and try again.
dr del