From your description this particular cross doesn't sound right for your family.
I work with dogs and if i saw a yorkiepoo
on the waiting list I'd be anticipating a nervous wreck of a dog with bad teeth that didn't know whether it wanted to jump into my arms for a cuddle or bite me defensively.
If your ds is anxious he needs a confident dog. I get your desire for a non shedder. I wouldn't choose either of those breeds. I think shih tzu as every one of these i have met has been laid back to the point of catatonia! however they tend to have expensive to fix eye problems so get ine that comes from a good breeder that has done all the health checks.
That is another issue with designer breeds, it encourages backyard breeding by people who haven't a clue and cross their poodle with their friends cocker spaniel because for some insane reason people are willing to pay more money for these crissbreeds than a pedigree dog whose ancestry can be traced for the purpose of screening for health issues.
In your shoes i would seriously consider a rescue dog. ive had rescues and non rescues and i would vote rescue everytime. But again a GOOD rescue that asks you lots of questions about your set up.
I think your Ds would get so very much from having a dog that he forms a bond with. But i would forgo puppy stages as they can be pretty stressfull. The play biting HURTS and might upset your ds.
I got a six month old heinz57 jack russel type puppy from the dogs trust. I suffer from anxiety and this little man was pertty nervous when he first met people but it was love at furst sight for both of us. Ive loved all my dogs, rescue or otherwise but he's "the one".
Good luck in your hunt for your new family member.