Submissive urination is a big pain in the butt! It's crazy because you want them to be submissive to a certain extent but you don't want the peeing!
I think that the best way to solve it is to recondition your dog to NOT be submissive when you are making the motion to pick him/her up. They should see it as a sign of security, and if they are hand-shy and submissive when you go to pick them up, they may have been conditioned that way in the past. The next time you approach your puppy, softly say their name and sound happy, have a treat in your hand, and give them absolutely no reason to be scared. Do this to the point where they in the "in between submissive" stage (semi crouched, ears back, but not rolling over, and tail wagging big time). After they realize that when you motion to pick them up you aren't going to admonish them or crate them (this was our biggest problem with Ritz-being picked up at home used to mean he peed on the floor and was going in the crate, now he's fine!). They will not see your actions as threatening and will no longer act submissive when you handle them or motion to pick them up.
There is nothing more irritating than a male dog rolling over and acting like a fountain-statue, or finding a puddle underneath your female every time you pick her up. Take slow steps and you chi will trust your hands!
-Nate
After re-reading your post, it seems like he's not afraid of your hands, so it's possible it's just bladder control he has to learn as a pup.