A lot of hotel booking sites offer free cancellation up to the day of the stay as an option that costs a few EUR or USD more. Business-oriented booking sites sometimes even have cancellation up to early evening of first day of the stay. (HRS.de is advertising this on TV right now in Germany as their main feature).
I would pay the few more dollars for that, get a room at the expensive rate, and then check back regularly, maybe even on the day you arrive. As soon as you find something reasonably cheap, cancel the expensive one.
This also works for flights, but those are often paid in advance, so you would have to fork out a lot of money to do that up front.
Also check international booking portals. You don't have to make your hotel booking through a booking portal that targets your country.
As mentioned in the comments, if you are not responsible for booking in your corporate setting, clarify this with your management, HR or whoever is in charge of booking, and have them do it.