At the end of 2010 I shipped my bike from Cape Town to Gatwick (London).
I used these people:
AMI (Air Menzies International):
Bradley: Tel: +27 21 935 1731
(I found this recommendation on a very old HUBB post)
Bradley did everything, arranged the crate and the crating, pointed me to customs for carnet stamping (a short walk from their depot), set up the shipment (on BA in my case) and gave me a tracking number, that worked.
He advised to remove front wheel, mudguard and handlebars, and panniers and top box to reduce cost (but all this is packed onto the crate with the bike, the idea is to reduce the dimensions).
There's plenty of space on their loading bay to do all this and his guys will lend a hand if you need one.
I'm not good at remembering details (I just had to look on the internet for his contact info) but the price was around 700 to 800 GB pounds (in local currency) which he took in cash. The deal was 'African' so to speak, informal with a hand-written receipt from a 'crating company', and afterwards I got the distinct impression I could have haggled the price down.
But I had an official paper from BA with the tracking number which was good enough for me.
The price covered everything up to collection from BA's warehouse at Gatwick but not the customs clearance at Gatwick (for 'personal effects') which cost a bit because customs is at Heathrow, it has to be done over their network with an expediter. If I'd shipped to Heathrow that would have been free I'm informed.
I guess for Zurich Bradley would use a direct Cape Town-Zurich airline.
I was very pleased with how it all went, Bradley's guys were very nice and helpful and careful with crating. And did the 'dangerous goods' certifying.
I phoned him to start and he invited me to visit his depot with my bike for initial weighing and measuring and it all went on from there.
His depot isn't easy to find, it's at the far end of one of the cargo areas. I can give you a set of GPS directions if you want them.