I have the same delimma, where the previous owner modified five of the cabinet doors by disassembling them and removing the wood inserts and installing frosted glass (yes, plain glass, not tempered). The glass was not tight and the doors were brad nailed/glued back together. I think I will wait until next winter and take the doors and have a local cabinet shop make new ones, using the original wood inserts (which I was given when I bought the trailer).
An alternative is to put safety glass film on the glass, which will prevent the glass from shattering if it is broken. I did pack screen wire spline in the gap behind the glass and that stopped it from rattling, but clear RTV pumped in behind the glass would be better.
In the end, I will get new doors, there is no chance of again disassembling these without destroying them.
So for the OP, my best suggestion is to use the glass safety film, such as this,
https://www.tapplastics.com/product/window_films/window_tint_films/safety_window_film/313Charles