Hiya,
My late girl, Evil Edna, was hyperthyroid, and because she was a little bit of a madam (well, a LOT of a madam!), tableting her would have meant finger loss!! I opted for a thyroidectomy (right side) and had pre-anaesthetic bloods done to ensure she was a viable anaesthetic candidate, which she was. Edna was late-teens, and I also put her on I/V fluids before and during surgery. She was absolutely fine after, and recovered really well. Obviously there is a higher risk the older the animals, so I highly recommend checking her kidney/liver on pre-op bloods and put them on I/V fluids, which all good vets recommend and offer.
Also, sounds like your vet's savvy about the op, as you have to leave the parathyroid in place. If they're stable on their meds this is better when the op is carried out.
I'm a vet nurse, and have seen this done several times with great success, so if I was in the position again, which I'm sure I will be as I take retirement cats on, I wouldn't hesitate if they're healthy enough for the op.
This below may also give you info:
http://www.fabcats.org/owners/hyperthyroidism/info.htmlLiz