is there a tool for CFW or for the PC where I can download the game updates or better yet, is there a way for me to stop the switch from checking for games updates?

I see, makes sense.Downloading updates requires a cert, wether extracted from the switch or on the switch itself. There is no reason to download updates for games you don't own so its treated the same as downloading games you don't own. Bans. There is no way to even inquire anything from Nintendo servers without likely getting banned.
you should def be on airplane mode to prevent connecting to nintendo servers unless you set up dns servers. 90 dns. airplane mode will not prevent a message to update a gm if it needs it to work. some updates if only small stuff you can choose ignore or cancel but they re easy to find if you look around. airplane mode will only prevent firmware update i assume. there are tons of game updates all over the internet. just google for them. they re nsp files just like any base game can be. installed same way. work with nsp games and xci gms.I see, makes sense.