Wii and WiiU games can't share the same USB HDD.
If you want Wii games, then you need to hack the virtual Wii mode, and use a FAT32 drive. (unless you inject the ISO into a WiiU virtual console, but then you'll need CFW after every boot, that's NOT what you want)
if you want WiiU games, then you need to install games to either the internal WiiU memory or a WiiU formatted HDD.
Before using any homebrew app, I need a custom firmware, which is what Haxchi is.
No, you don't need a CFW or haxchi at all to use homebrew apps!
WiiU games do not ALWAYS require a custom firmware, and the browser exploit alone is enough to play many WiiU games.
You DO NOT NEED haxchi.
You DO NOT NEED CBHC.
You DO NOT NEED to buy a NDS game.
you can do everything from the browser hack, but like said it can be a little hard to trigger the exploit and you might have to try few times/reboot the console/retry/etc.
but once the exploit worked, you can install games.
You DO NOT (always) NEED the exploit to play the installed games !
As long as you install games the same region than your console, and the game exists as disc version, then you don't need the browser exploit anymore nor a CFW to play it.
If you want region free, DLC, eShop games, then you will need to run the exploit + a custom firmware (not necessarily haxchi, there are temporary ones, like "simple signature patcher") to install OR play the games.
Please, not wiiu.guide (missing things, forcing users to do unneeded things).
He wants to NOT install haxchi and only use the browser, why providing a guide to do exactly the thing he doesn't want?