Sounds like you might have a toy motivated Yorkie, and that's a good thing when it comes to training. Instead of rewarding with treats, either toss a toy or play tug-of-war with a fleece rope toy.
If that works, you won't have to worry about weight gain or having to curb back the rewards later on.
If that doesn't work, try a better treat. Liver treats are a dog favorite. I even cut up tiny pieces of turkey dogs when I really want a reward that will drive them crazy.
As for chewing everything, try substituting an acceptable chew toy for an unacceptable one. If he picks up a shoe, give him a no and replace it with a bully stick or nylabone.
Good luck!
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