All joking aside, poodles come in several sizes and they are all clean, non-shedding dogs. I'm pretty sure that they were originally developed as one of the working dog breeds. I forget the actual mission/job of the breed...probably hairdresser or acrylic nail technician...
Standard Poodles were water dogs. The floofy poncy looking poodle haircuts were to keep heat on the joints and otherwise strip the dog down for work. Originally.
Jesus yes, avoid paying pure-bred prices for mutts! Shop carefully, check the breeder's references, and end up with a dog that turns out like you expected, rather than some random agglomeration of features from maybe both.
Remember also, any non-shedding dog means you are on the hook for a lifetime of payments to the groomer, if you are not willing to do the hair cutting yourself (also a not insubstantial cost in equipment if you want to do it reliably).
Should buy the wife what she wants. Yorkies are a terrier breed, complete with the terrier attitude. They may be small, but they act ten feet tall and bulletproof. They don't eat much, and if you keep them stripped down, they are easy keepers (as opposed to the classic show cut with the long draping hair, a PITA to maintain).
As a side note, I knew a woman that had 17 of the little buggers in her small home. Bath day for the whole lot was about a 45 minute job.
Get your wife what she wants, trade off the happiness to get what you want, and everyone ends up with what they expected.