Hi mel.
Crocs.
I know this might sound crazy at first but hear me out.
Many people think crocs are slippery and bad on wet surfaces but they forget that crocs were initially made to be water shoes!
There is a general rule: the softer the sole of a shue, the better the grip. If you look into trail running shoes you will see that some soles are made soft specifically for this reason. If the sole is softer it is able to bend and sink into crevices that a hard sole isn’t able to.
The only downside to the soft sole is that it wears away easier. This, however, isn’t really a problem for crocs. This is because the surface of the sole gets rougher as it wears down since it is kind of like a sponge that has thousands of little holes and edges that increases the friction between the rock.
Best option would be to wear wetsuit socks with the crocs. It ensures a snug fit and keeps your feet warm.
All this is me speaking from experience. I hiked up the drakensberg in crocs and I have done a few other several-day hiking tours in crocs. (with a 20+kg bag on my back). I also climbed a few mountains including victoria peak, matroosberg, helderberg dome and a traverse from stellenbosch mountain over to haalkop. If you don’t worry about ankle support then crocs is the best option.
No need for fancy approach shoes.
Edit: fixed typos