Using Spring AOP does not require AspectJ, so as long as you configure your application using Spring you should have no problems using the native JDK support (it's the default anyway). I'm not sure if you tried it and it didn't work for you, so maybe some more specific information in the question would help here.
Java Security Manager is probably a needless distraction, but maybe if you could explain what you meant to do with that in some more detail it might help as well.
And, by the way, I'm not sure what the overhead is that you mention with AspectJ, but if you think it's significant I would recommend testing first because it certainly isn't a big difference at runtime for most applications. It can even be faster than other approaches.