I would make sure the plastic container is big enough for the fish to not feel too crowded. You could maybe put a few pieces of rock or driftwood from the tank into the container while you change out the substrate so they feel a bit more "at home". But most importantly, cover the container and keep it dark. That will make the fish more docile and they might just sleep through the changeover. You should probably keep a heater in the container as well, and maybe an air stone or something to keep it oxygenated.
When I changed my dad's 55g from gravel to sand, I was going to do it your way, but instead I opted to just grave vac really thoroughly and then scooped it out, replacing with sand. I did half the tank at a time, and the fish never left the tank. They were pretty stressed out but within a day they were back to their old selves and looking active as ever.