Very timid and shy dog

Question
I adopted a 2 year old Chihuahua/Terrier mix breed dog from my local animal shelter about 3 weeks ago. At the shelter I was made aware of his attitude toward people and how extremely afraid and shy he was. I was told he came from a puppy mill and was used as a breeder dog so his issues mainly stem from his lack of human interaction. If he feels overly threatened he will bite at you but it's only if you reach at him when he's cornered (had to do so at the vet to pick him up.) The issue is that he's shy around everyone, even me though he follows me around everywhere I go and sleeps in bed with me at night. You can't pet him without his leash on and it's almost impossible to get a collar on him most of the time. I try to take him for a walk every day but somedays I spend 15 minutes trying to get the collar over his head without success and I'm afraid I'll stress him out too much or that his other lead pulls on his neck too hard. He will sniff people as long as they don't pay any attention to him but will not let anyone pet him or pick him up. I just want to know what I can do to help him become much less afraid of people, especially myself, and how I can make the collar and leash a much less frightening object to him so I can continue exercising him regularly. Thank you!

Answer
Instead of a neck collar (which he most likely has never worn), use a body harness.  This can remain on the dog all the time (or at least for the next few weeks, as he adjusts).  You can purchase a very short lightweight leash which he can wear on his harness in the house so you can direct him, or put his walking leash on, without cornering him, chasing him, or otherwise offering behavior which will most likely frighten (or terrify) him and disrupt the trust he will begin to acquire in your relationship with him.

Three weeks is NO TIME at all.  Your dog is still quite confused and not sure of his place in your household, let alone what it's all about!  It takes MONTHS of consistent, patient, loving and calm interaction with a puppy mill breeder (as well as many other sorts of abused and neglected dogs) for the dog to begin to relax and get with the "program".  Give this dog lots of time.  As for his interaction with others (on walks, visitors to your home, etc.), instruct people that your dog is a rescue from an extremely abusive situation and ask them NOT to reach down, touch his head, make direct eye contact, etc.  Instead, YOU carry small food treats (tiny pieces of chicken hot dogs or cheese).  If your dog approaches a 'stranger' to sniff, throw him a treat (toss it near him.)  He may not, at first, take the treat (because of overall stress), but eventually he WILL, and then he will begin to associate his own natural curiosity (sniffing and approaching) with REWARD, and his courage will increase.  Eventually, you may be able to hand the "stranger" the treat (or even a few at a time) and allow that person to (at first) toss the treat, then attempt to hand it to the dog (with an open palm.)  Let your dog learn to freely approach without fear before you allow others to behave in dominant ways (by bending over him, touching him, etc.)  Even if it takes months (through the summer into fall), the effort is well worth the result.  This dog could be the best companion dog you've ever had and might end up being a very friendly, confident little guy.