If it was me, I'd leave it alone for the time being. Blueing is no more protection against rust than bare metal. The wax you put over it and the care you give it will be the protection it needs.
I would take it and hunt it this season to see if you like it, if it fits you, and if you shoot it well. If it's going to be a keeper, then you can think about cosmetics. Moreover, if you put it in the shop now, you almost certainly won't get it back in sufficient time to use it this season. OTOH, if you wait until after the close of the seasons where you hunt, then you and your gunsmith will have all the time between then and next season to do the work. And you'll know if you want to keep the gun and spend the time and money on it.
Aesthetically, I'd be reluctant to go too far on refinishing because if you don't do the whole gun, it'll look like you didn't do the whole gun.
