I believe that the auto choke use an thermo-operated (bi-metal) reed type valve to change the port from cold to hot. I'm not sure if there's a way to be able to trick it, at least I've never considered it.
I suppose you could put a small manual valve between the appropriate two vacuum lines and do it manually. Maybe use a small valve like a drain cock from Home Depot. Close it to start and then open it to run. Carb don't know if it's hot or cold, only the head temp.
I can order the belt through the Honda dealer only it cost about $30! I found a really close one at the auto store for $11, but waited.