Usually all that is needed is just a little local anesthesia as its a very quick procedure (unless its a very large, very oddly placed growth).
As with anything, yes anesthesia can be a little more dangerous for an older dog. 6 isn't too old yet and he's in good health otherwise right? He should be fine, but if you are worried they can run a CBC (complete blood count panel) before he goes under to make sure he is healthy. That usually runs about $35-$55 ish. If you are interested in running the bloodwork I'd call them now & have it done tomorrow when you go in, that way IF there is anything wrong you can fix it before he gets it removed and he won't have to spend a whole day at the vets for nothing. You will need to fast him for that too, usually you just put up the food & water before you go to bed.

Its not pricey, I think the most expensive eye growth removal for Nanook was just over $100, the lowest one was about $65. Biopsy ran about $15-$25 ish.