I don't have direct experience with the Navy but we do with AF and Army. They will probably want to see any skin test data but will likely ask for a RAST blood test to see shat your IgE #s are relative to each nut. They ask you to do a alergist suppervised nut challenge.
I know the AF will not give a waiver for a nut allergy ,. . . no way . . . no how. You have to prove you don't have the alergay any longer.
The Army is more reasonable. They tend to loook at the type of nut and the severity of the allergy, history of reactions, etc.
I have been told the Navy will look at those factors as well, but I don't have direct experience with the Navy . . .
Best wishes to you and good luck. Let us know how it turns out.