With the multiman server being down, I can't use it to check for game updates anymore, but when I launch a game, I'm prompted about a game update. Are these safe to do?

Not entirely true, all 4.xx games/updates work on any 4.xx CFW, so even if you have a 4.30 CFW and you try to load a game/update requiring 4.40, mM would patch it and it would work.it depends on which firmware you currently are, and which firmware the game update requires.
If you are on cfw v4.40, and the game update require a 4.40 firmware or bellow, then it's fine ! the update will work.
If it asks you to update the game, it will only update the game (not the console's Firmware).
You can always delete the game update in the "Game data" menu at the top of the game column.
If you update a game, and now it requires a firmware you don't have, then it will ask you to update the console's firmware.
don't accept the console's update.
