You can't remove all the salt from a brine, as it then is no longer a brine. Mine is bout as low in salt as ya dare go. The salt is needed to perform osmossis, to pull the seasonings an yes some salt inta the meat. The sugar is there ta help balance out the salt.
With that said, ya can inject (Should be able ta get some sorta syringe, farm supply store, vet clinic er such. They ain't great but they will work. An injection is second best to a brine.
It works best if ya use both, but experiment.
Watch what ya use fer commercial rubs cause they got lots a salt in em to.
I'm not a big fan a stuffin a turkey an cookin it, but some do. If ya do, remember, that stuffin has to get to around 160° in the middle ta be safe. We always just make the stuffin in the oven, add some juice from a pan under the turkey fer smoke flavour in the stuffin, or cook the stuffin in a pan in the smoker. By the way, the pan a juices from the turkey make a very good smokey gravy!
Let us know if ya got any other questions, were always glad ta start ya in the right direction.