Actually, if you do intend to mod your Wii to get the save data. Online will be totally fine, as long as you copied your complete data.
Online only bans you when something is obviously amiss. Like an HR 7 with Rank 6 Armour.
If you copied your data and transfer to a new Wii, your online HR would stay the same, and going online will be no problem.
As the previous two have stated, there is no legitimate way to transfer data. Modding for backup save is the only option for a transfer.