I'm not sure about Honda Sprees. I have a PA-50 and the idle speed screw is blunt. You are right about the spring. I figure a spring suited for the task can be found or some other method of keeping the idle screw in place can be created. I'm assuming that the idle screw is just a throttle stop (like all Honda carburetors I've seen so far), in which case, I think a blunt bolt could be made to work.
The air mixture screw is definitely cone shaped, and as we both know, its shape and size are very important. OEM would definitely be necessary.