How do I play video through a projector without seeing the player buttons?

This is probably one of those questions with a really easy answer but either I'm not phrasing it right or there isn't a way to do what I'm wanting. At my church, we occasionally play videos from a MacBook Pro or our new 2019 iMac. The video pipes out to the projector just fine, everything works fine. The issue is when a video needs to be played or paused 300 people can see the mouse move over the Quicktime player's play/pause button. This seems very amateur hour but for the life of me I can't figure out how to play and pause a video in the booth without the buttons showing up on the projector screen. I feel like I saw a video on how do do this years ago, but I haven't been able to figure it out. Can this be done? Thanks!