So as I understand its day surgery and I won't have any down time beside the G Anesthetic
From memory, your next medical will ask if you've had an operation involving GA. While it might be colloquially said that you are having a day general anesthetic, technically, its more likely to be local anesthetic with a sedative. The experience for you is the same, but its a might lighter, safer anesthetic.
Regarding the specialist letter, in my experience CASA AVMED will not make any judgement calls and want someone else to cover their butt. Therefore they may ask for a specialists letter where HE states that it will not adversely affect your ability to carry out the functions of your pilots licence. When you see the specialist, I'd have a chat with him about whether he thinks it might be prudent for him to write one in advance of your next medical. Its easier for him / her to do it while his / her memory is fresh rather than needing to look up files in 6 months time.