Brine is literally salted water (think about the briny sea), so I would go with something different.
For something different and special, you could try grilling a turkey breast with a salt-free dry rub. Or for that matter, using a dry rub and roasting it.
You can buy the salt-free dry rubs commercially if you don't have a recipe from scratch.
I have a recipe for grilled turkey breast which the method is very good:
Brined Mesquite Grilled Turkey Breast
Don't use the brine in this because of the salt and don't try it omitting the salt because the brine then won't work.
However, here is a posted recipe for salt-free dry rub:
The Baron's No Salt Rub
Use the rub in the recipe for grilled turkey and you can add it at the point where you butter up the breast. Generally with dry rubs you would then want to wrap the breast with the rub on it in plastic wrap and let absorb the seasoning for a few hours, refrigerated, of course.
This is probably advice all to late, but there is always next time.
All the best-
~Sue