The risk of this depends on the surgery being contemplated. The risks associated with largyngeal surgery generally occur in the post-surgery time period so in this case the surgical time is not that risky. Older dogs recover at approximately the same rate as younger animals except that they are a little more likely to be sensible and take it easy for a few days post-operatively. Complications included post-operative hemorrhage, scarring causing obstruction of the airway, aspiration pneumonia and progression of neurologic signs despite surgical correction. Scarring would seem to be more likely with the removal of a tumor since there is less control over how much tissue is removed and which tissue is removed.
Hypothyroidism is a common complication in laryngeal paralysis cases.
Even low normal thyroid values should be suspect when laryngeal paralysis is present. If the tumor is already causing respiratory difficulty it seems to me you have little to lose by trying surgery, except the cost. If you can afford to have this surgery done without harming the care of other family members it seems to me that it is worth a try. Good luck with this. We have been treating it with buffered asprin as needed.