When I joined, I had the same thing happen to me. In the end I needed five waivers in total (my teen years were not spent wisely), but I still got what I needed and got into the Nuke program.
My recruiter also told me that I should sign up under a different contract, and that they could change it while I was in DEP. Now in my case, I was really just looking to join the Navy and wanted to go Nuke because it's what they needed (only later did I find out it was exactly what I needed too). I signed, they contacted me, and then I signed a new contract to be in the Nuke program. I later found out that I was the exception in these scenarios and not the rule.
My advice is not to sign anything that you are not ready to commit to. That waiver is not difficult to get, and they will hunt it down for you in order to get you to sign on the dotted line. If you sign a different contract, and they decide that it's good enough just to have a warm body fill a position, then you could be stuck with the rate you've committed yourself to. My point is, signing that contract does absolutely nothing for improving your chances for getting into the Nuke program, and may actually be a detriment. If you won't be happy being a Fire Control Technician or Torpedoman then don't sign up as one.
Good luck and keep us posted,
Bradley