Suzuki 400 Burgman choke

It's a long shot but does anyone know if the auto chokes on these carbs Keihin CVK are the same irrespective of carb size?
The Burgman has a 36mm carb but I have seen very similar choke units listed but for smaller sizes up to 30mm.
It is similar to this type
http://www.ebay.co.uk/itm/Electronic-OKO-cvk-Auto-Choke-Bi-Starter-Cold-Start-26-30mm-/301435522904

 

The genuine Suzuki one is £93 + vat

 

Well I got the old choke out and measured it and it appears to have the same dimension i.e. 20mm and 7mm plunger so I'll give it a go.
A lot cheaper than the genuine one lol
If anyone knows of a cable conversion for this carb let me know.

 

Its an odd size that choke, same as the carbs on the vx125's, struggle to find the 7mm ones