I do not exactly know what the cups-control slot is offering and for what it is good for. It is not made by me and not with my cooperation. It was simply there when I looked into the snapcraft documentation for the first time.
I am working on snapping the CUPS printing stack, see this thread. This snap does not provide any slot (yet).
What is needed for CUPS access (printing, listing printers, jobs, and options, also administration) is both access to the domain socket of CUPS and localhost:631. In reality only one of the socket and localhost:631 is needed but one does not know which of the two the local CUPS offers by its configuration.