Can you manually force a trigger to fire?

In short, no. 

Manually forcing a trigger would require changing status or other information that would prompt a trigger to fire. This will mess up with order flow and all the background processes that depend on the order status. Most noticeable to you, it will change the dates that the order was moved through those statuses which would definitely impact any reports that you pull for those orders. 

If you think you've found a way to force a trigger to fire without messing with dates or statuses, run it by us in the support chat and we'd be happy to think it over for you to make sure you don't interrupt the normal flow of business!