Hi. Sorry your pup is having problems... and I haven't read this entire thread, so my apologies if I offer advice already stated...
My first question is: Does he eat enough to keep weight on?
Allergies can produce excessive mucous (shampoos too), and scratching the muzzle directly after a meal is an allergic reaction.
I have read that you have tried many different types of food, and that none are working for very long. Chicken is the #1 allergen in Yorkies, if you've eliminated that and he still has a problem, eliminate all fowl. Then start eliminating grains, and change up on the protein source. There are diets sold at Petco and PetsMart that are made specifically for dogs with allergies. Does Timmy scratch after eating home-cooked chicken? If no, then I would assume an allergy to a preservative as opposed to the food itself. Eliminate all foods that contain any meat meal (chicken meal, beef meal, salmon meal, etc.) as an ingredient. These are processed differently, look for human grade ingredients.
Also, any food you buy from Petco or PetsMart can be returned for a refund/exchange if your pup cannot eat it, there is no need to finish a bag if it is causing him problems.
With that said, any food you feed can be liqufied in a blender (I'm sure you know this). I would also put some probiotics in his food, this one mixes well with water too.
Nature's Farmacy - Store - Product Details
I would use it for any pup with digestive issues... you may want to discuss using it with your vet first.
Also, maybe homecooking (with the recommendations of a nutritionist) would be a better way to go with him.
I can understand you not wanting to do the surgery at this time, but maybe an appointment with a nutritionist would be more helpful in getting him to eat better.
One more thing to consider... I have heard about 2 different dogs, one in MD and one in PA, with allergies so bad... the Dobe in MD was eventually PTS, it couldn't eat anything, and had been through everything vet medicine could offer... the other dog in PA had some horrible skin issues from allergies, nothing worked and the pup was just miserable all the time. The owner ended up surrendering her to Dog Town, and surprisingly the change in the evironment cured her problems completely. These are both sad outcomes for the owners... I always wondered if the Dobe could have been saved if she had been sent to a different part of the country (before Dog Town), but it would be something to consider if your dog's allergies are also environmental, for his health.
And, again, my apologies if I have repeated anyone else's suggestions... I hope you can find something that will help him...
Oh and no plastic food or water bowls, and maybe try an elevated food dish for him...
http://veterinarynews.dvm360.com/dvm.../detail/693009