The Photo Channel is a valid channel with a valid banner. I think it is highly unlikely to (banner) brick the Wii Mini.
Since the Wii Mini lacks the possibility of software base NAND restore (to my knowledge at least) I refuse to do tests into that direction. (Yes, I'm willing to loose a console for testing purposes, but only if there is any potential benefit worth mentioning). I see virtually no use for the Photo Channel without an SD slot and am not willing to try it.
The very least you should have before any modification beyond the Homebrew Channel is the latest Priiloader version and a USB keyboard to bring up Priiloader menu. Make sure you have a Wii Remote synced to the Wii Mini in order to use homebrew apps. Priiloader can be controlled with the USB keyboard – but to my knowledge no WAD manager.
Sadly there are very few replies on any topic/question concerning the Wii Mini. Have had the same problem when searching for help on installing cIOS and crashing Syscheck.
It will work fine, just like every Wii application title (as opposed to IOS), indeed it is the special exclusive IOSes's job to simulate the only dealbreaker (missing wifi card) to the extent necessary not to break existing software