Not sure what your debt status is but, speaking from personal experience, I know that they can get you a waiver for your age; I was 27 when I joined. DO NOT SIGN ANYTHING until you get what you are looking for. If you want to be a Nuke, and the recruiter is saying that it's easier to transfer you to Nuke after you sign up as a (fill in the blank); it's a lie! It's easier to get what you want if you give them nothing but what you are willing to give. You aren't playing hard-ball, you're just being honest about what is acceptable. Now if you don't mind being signed up as a (fill in the blank) then, by all means, sign on the dotted line.
69 is a rough score to work with. At least it was when I was going through. The lowest score I'd ever heard of getting into the program was a 68, but that guy blew the doors off of the Nuke placement test (it's a secondary test that focuses on Math, Physics, and all other Nukie necessities.) That being said, it is possible. It is also possible to take the ASVAB again. You can take it a certain number of times per certain time period; I forget the specifics. You may have an altruistic recruiter that will tell you all of this, but most recruiters I've heard of didn't fit this bill. (I never had to deal with it personally, because I was rushed through the process when I joined shortly after 9/11.)
Point being, agree only to what you would be happy with. When and if you get accepted, be ready to work harder than you ever have before. Being smart doesn't guarantee success in the Navy, hard work does.
Good luck, and keep us posted.