The ch440s , at least those on the stihl rb800 pressure washers, do have a quirk.
Instead of the bowl vent for the carb being routed at the front of the carb, venting between
the carb and block insulator like honda/ predators, it is instead ran over to the air filter side of the carb,
and the air box has a nipple that goes into the carb so the bowl vent can, well, vent.
So if you install an aftermarket air filter adapter, you may need to do some modification
with a Dremel tool so the vent is not blocked.
If nothing else, you should be able to remove the kohler carb and install a gx390/ predator 420 , ect
carb on your motor and not worry about it.