What is the reason for wanting the nail removed?
Is it broken or painful?
The groomer can trim the nails down but removing them is not a option. You can consider using dog booties as well until he is fully trained and has calmed down some. You can also make these booties your self by using baby socks and sewing Velcro on to the top to keep them on.
This is the best way to handle the situation until the dog can be fully trained from this behavior. Now for the training........you can use a shaker can to get his attention and firmly tell him NO when he starts jumping and scratching. (A shaker can is a bottle with loose change in it). You can also use a spray bottle with cool water to spray him while firmly telling him NO.
The good news is with a little time and training he will learn this is not OK and the booties can be removed.