The VM Mikunis doesn't actually have a choke as such, they have a Starter System / fuel enrichment system. A proper choke is actually a butterfly or slide valve in the carbie that will restrict the air flow and and thus cause a richer mixture for starting.
On the VM Mikuni the Starter System and pilot circuits are two independant systems. Changing pilot jets will not affect the fuel mixture when using the Starter System. Also, the Starter System will only work if the throttle is fully closed during starting.
The Sudco Mikuni manual, state; "At tempratures above 68 F, the engine can be started without using the starter." 68 degrees F is 20 degrees C, so it would have to be fairly cool to actually need the "choke".
If the mixture when using the "choke" is too rich, there is a Starter Jet within the starter system. I have never replaced a starter jet, and don't even know if you can get alternate sizes.
Altering the air mixture screw or changing to a smaller sized pilot jet will only effect the fuel mixture at idle and at the initial openning of the throttle. So if you engine run ok once it has been started, then the pilot jet is the correct size.
CJ