You’d want to be in a bloody good sized boat due to differing weather conditions as you “round” the headlands.
I have researched a bit for you and find that Pigeon Bay is 21 “miles” from Lyttelton (by steamer, lol!) (33kms) and that isn’t even half way. My estimate from knowing a wee bit of the territory and having been about half way, is in vicinity of 90kms.
As a suggestion, give a charter boat operator a call or better still, try the harbourmaster at Lyttelton (freecall from ChCh) or toll call to Akaroa harbourmaster.
It will be interesting to find out so please post the result when you get it. Good luck and take a good lunch with you.