I'm very sorry to hear that your degu is ill! I know how difficult it is to go have a degu who needs serious surgery. I've had two operations on my degus, one for an eye infection and one for cancer and both were successful. Its difficult because we are told the risks of operations are higher because they are small animals... BUT...I think that your vets sounds like he know what hes doing, to be able to dignose this in a degu. He sounds like one of the good ones!
I'm sure you won't want your degu to suffer, and its up to you to decide which is the best option for him. You will have support for which ever decision you make from many people here. BIG HUG!!
I also think you may have helped me, because my degu, Rum, has had very similar sounding problems for a while now, and has been on various antibiotics (Septrin and now Baytril, along with numerous injections, for a chest infection which refuses to clear up). Both he and his brother are notorious for having tooth problems too... I will be phoning my vet on monday!