I’m a vet, so hopefully can help a bit.
There are two types of pyometras, open and closed. You’ve said your dogs is open, which is good. In my experience closed pyo’s are the cases which are much higher risk, these dogs tend to be very ill, and more risk of sepsis, rupture etc. Open pyo’s don’t tend to be as concerning in the same way.
I don’t want to step on your vets toes as I clearly don’t know your dog, and maybe there are factors that mean they feel the risk is higher, and they are right to warn you off risks, but personally I don’t tend to be too concerned with open pyo surgical risks.
12 isn’t ancient for a shih tzu, but is obviously an older dog, I would generally recommend bloods to check there are no other concerns (not just due to the pyo, I recommend if for any older dog having a GA), and a drip. Provided that’s all ok then, yes, there is a risk still, but I wouldn’t say particularly high.
I generally advice 10-14d recovery post spay, and unless the dog is really unwell (generally closed pyo’s), I don’t tend to find this any different for pyo spays rather than just a spay.
It absolutely needs treating, either medically (but then still spaying as will generally happen again after next season), or surgically. From what you had said surgically treatment sounds appropriate, but euthanasia is not a wrong decision either if financially or for other reasons you decide surgery isn’t right for your dog.