the poll is not really needed, you need only one "yes" to achieve what you want.
But yes, it's possible with two different ways.
Ps: I'll edit

I'm writing a small guide.
so you know : MicroSD 1GB is just fine. what's your problem with it?
So, first, you don't need to install the HBC on WiiU, but you will need to use it (no need to install it as a channel).
What you need :
you need 5.5.1 or 5.5.2
you need haxchi or CBHC, or if you really don't want to install that, you also can use the browser hack method. just know browser hack is less stable and require more tried on 5.5.2.
Method 1: WUPHax
with this method, you will replace the vWii "Mii maker channel" code with a "elf booter" code.
then, launch vWii, run Mii maker, and it will load hackmii installer's boot.elf located on SDHC to install vWii HBC.
after the install you need to restore the original Mii Maker channel's code, or you'll lose access to edit/create miis forever !
the Mii maker channel's code replacement is done on WiiU mode, with a WiiU homebrew.
tool :
https://github.com/FIX94/wuphax
Official release and help thread here :
https://gbatemp.net/threads/wuphax-v1-1-hacking-vwii-from-wiiu-mode.446786/
Method 2: WiiU wii virtual console game injection.
If you already know how to create WiiVC injected games, it will be very easy.if you don't, it's still easy.
You will have to create and install a channel on your WiiU which will launch vWii mode and launch a WAD manager.
from the WAD manager, you just install the open source HBC wad file.
you need this :
https://gbatemp.net/threads/release-wiivc-injector-script-gc-wii-homebrew-support.483577/
you need this :
https://github.com/FIX94/Some-YAWMM-Mod/releases
You need this :
https://github.com/FIX94/hbc/releases
inject the boot.dol of "some-YAMMM-Mod" into the injector with the "homebrew mode".
install the created channel file with WUP installer GX 2 on WiiU
launch the channel and install the HBC wad.