Instead of disabling auto-updates you can also clear the default gateway on the printer. No gateway = no Internet access, but it's still LAN addressable.
I have a Brother printer with wifi. The day it upgrades and block me from using reasonably priced toner, I'll set up to a Raspberry Pi as a print server and hook it up via USB. I'm wondering how much of a market there's going to be for this and if cheaper devices could be used.
By then it would be too late. Alas it seems Brother doesn't do these things. It's HP. People should stop buying their products.