Is the waiver because of the arrest record or something else?
If for the arrest, just keep in mind that the paper investigation to get a secret clearance is not the determining factor in whether you get clearance. It is just an investigative process. The final authority will be the Navy and the nuke program. What I am saying is that if the Navy grants you a waiver following a review of your arrest record, then they are the same authority that will grant you the necessary clearance.
In essence, you will have been pre-screened on this issue.
The important thing is to be extremely honest in discussing this and other issues that would impact you ability to get a security clearance. Also be aware that when applying for a security clearance, you must grant the service the ability to access any and all of your personal records, even if sealed by the courts, as well as references, employers, school records, etc.
The bottom line is that what you did pales in comparison to drug and alcohol, or financial abuses, or having close contact with foreign nationals.
This does not mean that your actions back then will be forgotten. It will always be there as a 'black' mark on your character.
By the way, there was nothing in the nuclear engineering spaces above confidential that I encountered during my nuclear service. Now when I went to the conventional navy and into operations, especially in the radio room, they got real serious in clearing me for Top Secrect and access to spaces containing messaging and the equipment painted red.
Oh, be assured that you will have your security clearance either before you get to A School, or shortly thereafter, and certainly before they start training you on classified equipment (ie ET's and control and instrumentation).