A twin humbucker guitar shouldn't be particularly noisy to start with, even without cavity shielding. In addition to WeirdBits suggestions, check the potentiometers for smooth travel. It's possible that you may have overheated one or more of them when soldering the ground connections to the casing. They normally end up feeling a bit rough and scratchy if you have. I've done it before, despite trying to be careful.
But it still could simply be that you are testing it in an electrically noisy environment. Any other guitars/basses that you can use for a noise comparison test? Any nearby electrical equipment that you can turn off (including lights - especially fluorescent lights or those on dimmers)?