My german shepherd puppy gets excited when she sees my husband. She pees more than just a little spot. I'm not sure when it will stop, some say when they get older.
Alot of dogs do this when they get excited/nervous. Be calm when you approach him and don't just immediately put the leash on him or pick him up. Just give him a minute to calm down. My boyfriend's mom's dog does this whenever somebody she isn't used to comes around. I used to be scared to pet her because I thought I was gonna make her pee, but I finally learned that I have to just ignore her for a minute and then pet her when she calms down.
Your pup seems to be very afraid, try doing positive training with him/her. Say your dog's name and if you get any response (looks at you or tail wag...anything) reward him with a treat. Also do this before you put on the leash or before someone picks him up. Your dog needs to know he/she is safe and loved. Try to avoid saying "no" and try saying oops.
Chihuahua's are very timid so I'm sure that's what it is. Try behavior therapy & get him used to the tuings that he doesn't like by slowly introducing them to him over & over until he is not so scared any more.
If you vet rules out physical problems then it sounds like he is timid and easy to intimidate. Frequently dogs that are timid will pee to show submission or as a nervous reaction. My friends little dog will pee when excited also. Hope this helps. jaymac