B.A.
First of all, good for you for not circumcising! I'm very grateful to my in-laws for researching circumcision and deciding against it.
Second - if it really is a shaking off issue then you can always have him just dab the tip with a single square of toilet paper (so he doesn't use it up too quickly) which should take care of any dripping problems. My husband sometimes dabs if just shaking doesn't do the trick.
I also agree that vinegar is great for pee smell. We cloth diaper and use vinegar in the wash when they start to smell strongly.
Best wishes!
~B.