If the Vet feels this needs surgical removal, it is very unlikely to come off with topical applications--which is the only "home remedy" I can think of for wart/skin tag/mass removal on a dog's eye. The mass is most likely to continue to grow and possibly cause problems down the road (dry eye, corneal ulcers etc.), especially if she rubs it.
You are at an advantage right now because it is (I presume) small and she is 9, which is a good age, she's healthy and has a caring owner. This is most likely what your Vet is seeing and thinking.
But, I do understand your concerns with anesthesia. There is always a risk. To help reduce the risk, if you do plan on going forward with the surgery, ask for pre-surgical bloodwork, an IV catheter and LRS during the procedure.
I'm definitely not encouraging you one way or the other. It depends on you and what you can deal with. And believe me, I understand it's easy for someone else to say "Oh, just put your dog under and do the surgery" But it's not their dog that's taking the risk, not them experiencing the conflict (risk of anesthesia vs. health of the eye). Speaking more in depth with your Vet and voicing your concerns may help you choose the path to move forward.
I wish you all the best and good luck to you and her (she is a very gorgeous dog!)!