You could, but that's not ideal. Here is what I recommend.
1. Run mover, verify only things left on the old cache drive is the docker image and empty folders, no real data.
2. Stop array, unassign cache device, shut down, physically swap cache drive, power back up.
3. Assign new cache device to slot, start array, format new cache drive, set appdata share back to cache prefer, run mover.
Now, you have a choice to make.
Allow unraid to create the docker image file as it was, on the cache drive root. That choice will happen automatically when you enable the docker service if you make no changes.
Or, create a new cache prefer share that will hold your docker image file, and set the image file location to that new share. I think the defaults are to have a share called system, so the docker image would be /mnt/user/system/docker.img
Either way, after you enable the docker service, go to the apps tab and click on previous apps under menu on the left, and select all the apps you want to put back.