Hi George44331! I think we can get you to the same result in one step instead of two by using meeting polls. Tutorial on Meeting Polls → Create and Book a Meeting Poll

Basic workflow for this

• You would create a meeting poll for both the contractor and customer to find a mutual time.
• Then book the meeting. 
• If you don’t want to meeting on your calendar, you should be able to reassign host duties from your calendar. 
• Other option in case you want that booked time slot freed up - You can use the Book Over feature on your other events to tell them to ignore that event as a conflict. 

You have a second option

You could also create a Collective Event Type with the contractor as the second host. This event type is designed for when there are multiple hosts but one invitee. The benefit here is that the contractor would connect their calendar to the event. Then the customer could choose from the available times. While a little extra work, the other benefit is that this event type also supports polls and would be ready to go in the future if you continue to work with the same contractor. More on Collective Event types → Setting up Collective Events