JMO, it would have to be an allergy that really was bothersome with no treatment available to not let my pup outside. Since dogs are pretty much wolves, I just don't think it's fair to them to expect them to stay in the house all the time.
But I also don't think Yorkies should be allowed to hunt, eat random things outside, etc. So unless there is close supervision, running around outside probably isn't a good idea. How about leash walking? Yes, allergy testing is a good idea. If it is presumed to be environmental and you really don't want to test, then you could talk to your vet about Atopica (although it is an immunosuppressant and very likely not healthy, esp. long term). Ellie loves it outside. She be devastated if she couldn't go sniff.
