I am sorry to hear that your boy is having those problems.
Some of your concerns can't be answered without looking a little further. I don't think that 10 is too old for surgery, but the question becomes, is his heart healthy enough?
If the only thing that has been done are X-rays, I think that pursuing an echocardiogram would be a good plan. This will allow function to be assessed. (X-rays can be misleading especially in little dogs like Shih Tzus.) After that is done, a much better answer can be given to the question about how safe anesthesia and surgery are for him.
The other problem that I frequently see in the brachycephalic (squished face) breeds as they age is tracheal collapse. Here is a link to an article on tracheal collapse:
Additionally, assessing his weight may be a concern. Obviously, I haven't seen him, and he could be very lean, but many of these guys get a little heavy. Weight loss makes major changes in many cases!
I hope this helps!
As always, if you have further questions or concerns, please don't hesitate to ask them using the "reply" function.