Remember, the only thing generating any heat in that pic is the dust in the AMNS which generates very little heat. The smoker's heating element is not on. It sounds like you are going to attempt to burn your chips dry using the smoker's heating element but with a pan of ice? That will not work for cold smoking, especially of cheese.
What cmayna said. The plastic won't melt with just the AMNS burning, or with the element at 100° with the ice in between, but I would recommend just the AMNS or the AMNPS.
And the jug of Ice if the ambient temp is high.