I doubt that this could be fixed with an update. It would require the actual firmware to be updated, and most flashcarts don't have the capability of doing that (the updates that people refer to as "firmware" are usually just menus and rom loaders).
There are a couple of ways around this. The obvious one is to flash the DS so that it never shows the health & safety screen.
The other method is to set the system to start the game automatically, then remove the battery to clear the personal data. When you start up the system it will go through the initial setup again, and as long as you don't press A to power down the system and finish the setup the DS will always bypass the health screen and load the flashcart automatically.
The downside of that method is that until you finish the initial setup (thus undoing this trick) you won't be able to get into the DS's menu to change settings or use download play or pictochat.