Of course you need to do what 'you' think is best.
But here is 'my' spin on the real old dogs. They are near there end of their life and unless the teeth are causing extreme infections where the infection will cause them to die sooner, I do NOT put my old guys under for teeth cleaning or extractions.
IMHO "JMHO" some vets are just way too quick to tell you you need teeth cleaning regardless of age. Heart and kidneys are just not up to snuff on an older dog. And what is the base line they use for an ok heart and kidney function to go under? No one knows, it depends on each dog and their age, not a number on a blood work up. I just won't do it.
And of course the vet is always first to tell you that bad teeth cause heart problems. Well my dogs are on their last part of their journey and sadly but reality they are going to die before a bad tooth is going to affect their heart enough to make them die, and I just won't take the chance of loosing them to a teeth cleaning.
About tumors. Talk with your vet. I was told by my vet that once you open up a tumor and/or aspirate it to check for cancer cells or to remove it it then spreads like wildfire.
I don't have the technical words for it but when tumors are exposed to air is what the culprit is. When tumors are removed on people it is done so in an environment and with special equipment that no air is exposed to it during removal.
Vets do not have that type of equipment to do surgery with. Nor have I met a vet other than my vet that has admitted to that fact and the consequences.
Again non medical explanation. So, I don't go in or aspirate tumors on old dogs. Unless they are impairing their quality of life. Just saying it's what "I" do. Every pet owner and dog is different.
My advice is don't just do what the vet tells you, ask you vet questions, tons of questions, until you are satisfied, before you decide. :C