I'd suggest that if you're right handed to load with your right hand and hold the gun with your left. I'd also suggested standing closer to your 'gun' so that he doesn't have to turn towards you to swap guns, thus taking his eye of the birds. Don't be afraid to stand in close!
The problem with Safety Catches is the name. All the safety catch on a shotgun does is to block the trigger. It does not block the firing pins, so the gun could still fire. People ignorant about safety (like this man) are seduced by the name, so they love to tell everybody to always use the safety catch. They usually love a bit of virtue signalling, particularly if it involves some ostentatious melodrama. In the video situation i.e., double gunning with a loader and a gun, you really need to understand what credible accident you are trying to prevent by using the safety catch and that needs to be balanced against the downside of getting someone to concentrate on using the catch, when their mental attention would be better directed at something important (from a genuine safety perspective). If I had a loader twittering at me about using the safety catch when double gunning, he would very quickly find himself banished from my peg.