you dont need to even install HBC to get the save data. you can run a dol from bannerbomb and it will already have the necessary permission to read the SSBB save data. theres no cIOS or exploit needed. you also have permission to write save data for that game.
so, if it were me, and i wanted to do this without installing any homebrew, heres what i would do...
1) use smashstack on the old wii to start FTPii. as long as you use a recent version of the program ( one that doesnt reload IOS ) , it will be able to read the SSBB save data.
2) copy all that data to your PC using ftp.
3) use the tools from sehger's git to pack the extracted saveinto a data.bin
if you go this route, you will not be able to copy the stuff in the "NOCOPY" folder to the new wii. but i think thats only stuff that depends on WiFi anyways
4) use the system menu on your new wii to install that data.bin
however, if you want to copy the stuff in the NOCOPY folder for whatever reason, you would want to do steps 1 and 2, but instead of creating a data.bin, you would want to run smashstack on the newer wii and start some little custom made program. and here you can write back all the game data including the NOCOPY folder.