Older dogs can develop benign nodules in their liver that can cause the liver enzymes to increase a bit. Dental disease can also cause elevations. So if other testing to rule out things like Cushing's disease, diabetes, etc were all normal, I wouldn't be too worried about anesthesia.
Dental disease, and all the bacteria that gets into the blood stream, can cause a dog to feel pretty poorly. So you do need to weigh that possibliity against the risk of anesthesia in an older dog.
But 12.5 yrs in a Scottie isn't extremely old. If Archie is otherwise doing well, I would certainly recommend a dental cleaning if he needed it. I would do pre-anesthetic bloodwork to recheck the liver as well as look at kidneys, complete blood count, electrolytes, etc. I give all my patients under anesthesia IV fluids during the procedure to keep them from getting dehydrated. Depending on his mouth, I might start him on antibiotics prior to the dental procedure, to decrease the amount of bacteria.
The other thing about those liver enzymes--Scotties are known to have higher alkaline phosphatase values normally than other dogs. So Archie's liver may be perfectly normal!
Yes, I had one Scottie patient with deplorable teeth. I diagnosed him with a stomatitis and managed it with chronic metronidazole antibiotics and the occasional teeth cleaning. The owner also brushed his teeth daily, which helped. But his liver enzymes were always high, prompting me to do some research. So I suspect Archie is just a normal Scottie!
You might ask your vet about giving him something like alprazolam prior to the vet visit (or groomers) to help decrease his anxiety.
If he has overall anxiety, I would ask about using something daily/long-term--maybe prozac or similar.
Well, they can be both assertive and have anxiety. Scotties are a stubborn lot! At least worth discussing with your vet. Maybe see how the alprazolam does short-term and if that seems to help him overall. You can always start on something long-term.