I certainly understand what an ordeal it is getting Pekoe sedated, and I share your concern about all the drugs. First things first though. Earlier today, I mentioned 'tarsal gland adenomas', they are also known as 'meibomian glands adenomas'. These still seem to be what you are describing. Here are two excerpts. If at least you have a better idea of what these growths are called, and how they're treated, you'll be better informed when you get to the doctor.
"Meibomium gland adenomas. These small growths are commonly called 'eyelid warts'. They are very common on the eyelid margins of older dogs. They are small tumours growing from glands which open on the edges of the eyelids. When tiny they may not irritate a dog, but as they grow they rub on the cornea, causing irritation, discharge and then ulceration. They need to be removed surgically. It is not sufficient to cut off the visible wart. The root of the tumour in the eyelid needs to be excised as well, so we will cut a triangular piece of tissue out of the eyelid. Cosmetically this looks very good, even for quite large tumours. However, as with all growths, the earlier they are dealt with the quicker the surgery and the less disruption to the patient, so if you see one on your dog, seek advice sooner rather than later"
"Meibomian gland tumors are tiny, slow-growing tumors that form in the meibomian glands of the eyelids. (Meibomian glands are sebaceous glands that provide an oily secretion to stabilize the tear film over the cornea.) Common in older dogs, meibomian gland tumors are usually benign, but a small percentage of them are carcinomas that can metastasize into lymph nodes.
Meibomian gland tumors can protrude outward or can extend into the eyelid. Some of these tumors will become ulcerated. Some will cause keratoconjunctivitis (an inflammation of the cornea and conjunctiva). Benign tumors generally do not spread, but they can become inflamed, irritated, and painful. If the tumor becomes large enough, it can cause problems during blinking (resulting in extra tearing and tear staining). Most meibomian gland tumors grow slowly. A veterinarian can detect them easily because of where the tumors are located.
Treating the Tumor with Surgery and Cryosurgery Many of these tumors can be completely removed with surgery. If the tumor isn't completely removed, it may continue to grow. In many cases, only a mild sedative and local anesthesia will be necessary. The larger the lesion, the more likely that general anesthesia will be required. Cryosurgery (tissue freezing) may also be used to ablate (remove) the tumor."