Sadly that is not possible due to how the Unending Journey works - it's not simply a recording of the first time you play through that event, it is literally reloading the cutscene into memory. Most cutscenes can get by fine with only the player's character shown in them, but the Ceremony of Eternal Bonding naturally requires both the player's character and their partner at the same time to work - hence the Unending Journey cannot reload it with only the player viewing it.

Sadly unless you record the scene externally using third party recording software for the PC version like FRAPs or use the PS4's 'Share' video capture function when you actually attend the wedding, that scene sadly is gone forever I'm really sorry to say. I definitely sympathize though - it's why I took a ton of screenshots when I had my own wedding and arranged several of the guests who were invited to record the video for it too, so it wasn't lost for this reason.