What you should do is use ModMii to install IOS 62 & Shop Channel 21 (if you don't have these), then go to the Shop Channel and look for the Wii U Transfer Channel (free download). Now I can't confirm if this will be safe or not but I have spoken with a number of people here and on other sites who say they did it and all was fine. I'm told it will not transfer any hack related material (IOSs, custom channels etc etc), nor will it effect your Wii's mod. It will however permanently remove any game save data and purchases you've made in the Shop Channel as well as your points and place them instead on the Wii U (I'm sure you know this already but I'd like to cover all the info I can lol).
Again, I can't personally confirm this so maybe waiting for a 2nd opinion is the best choice before actually doing the transfer. But based off what I've been told there is no risk to it...only reason I've not done it yet is I have no where to leave my Wii U setup and don't want to retire my old Wii until the U is hacked and able to run Devolution with emulated controller and memory card support...I simply can't go without the ability to play my GameCube games
If you want to post a sysCheck that would be good just so we can see whether or not you may already have IOS 62 installed (I'm guessing you don't), but to be a bit more direct to something you said in your post, you do NOT need to update the system menu...all you need is IOS 62 and Shop Channel v21 (SCv21 is how you get the transfer app).