By non-adjustable, do you mean it has rivets instead of screws holding it to the housing ? If so, those rivets can easily be removed and replaced by screws. Or it's something entirely different that I've never seen. Hopefully, someone more familiar with a California emissions carb can chime in.
What actually makes the choke a pain ? It doesn't stay on long enough ? Maybe you idle calibration is way too lean to start with ? Maybe the idle tubes are partially clogged ?
Welcome to the forum by the way.
Don't forget to include your carb number in the next post. It's stamped vertically on the driver's side, probably look like: 17058xxx
Frank.