The HD Loader is an application (.ELF) for your PS2 that you can run off your memory Card, an USB Stick or a CD an then load your games off the Hard Drive that you can connect over the Network Adapter with you Fat PS2.
I don't have a wii u anymore to test it myself, but if homebrews are not visible on the wii u menu I think you can press L + R + minus to open the plugin menu, there should be an option called "homebrews on wii u menu" or something similar