I think the ideal situation with the Sanparks hikes is to find a trail where there are going to be enough other hikers that you wouldn't be hiking truly alone. Some of them are more remote than others. Generally, yes, the wildlife is not the concern (although in a few places, it might be), it's crime. It's going to vary trail to trail, but some of the trails actually go through/near villages, so you are not necessarily all that far from human settlement. And one of the legacies of apartheid is a history of violence, even in rural areas (and particularly KZN/Eastern Cape). I'd browse the Sanparks website, then call up the offices of the trails you are considering and see if they have advice for you on safety and when a good time to visit might be if you want safety in numbers. I do think it's possible to do safely, with some planning.
On safety in general - you want to take the warnings seriously. Crime rates in South Africa are no joke. However, they also vary a lot. Highway rest stops are actually generally super-safe (though stick to the ones that have a gas station, not the ones that are just a bump-out with picnic tables). You don't want to get stuck on the side of the highway if you can avoid it, but that has happened to me, and I've had flocks of kind strangers descend to help me out. Downtown Durban and Joburg have crime, but more of the mugging variety than the abduction/rape variety. I do walk around in the CBD of both cities, although I wouldn't take my valuables with me, and I know which areas to avoid. Stick to places that have lots of people in them. I would never ever go out in either of those places as a pedestrian at night, or walk down a deserted alley during the day. South Africa is actually very different from most of the rest of the continent in this respect - crime rates, particularly for violent crime, are much much worse. Lesotho itself is much safer - and also has cheap organized hiking/camping/pony-riding treks. Bulungula also has organized hiking options, although maybe not multi-day.
I think you are right to avoid the Baz bus - it's expensive for what you get, and you'll be much more constrained.
Good luck planning! South Africa is a complicated place, but super-interesting for that very reason.