Few things I see here.. Touch up paint is fine to use, just be very careful when applying it.
I'm not sure what "cleaner wax" is (maybe just marketing?) but that buffer you should be very wary when using. I have no idea what that is but it looks like it can be paint damaging. You have to be careful when using buffers like that because they can burn right through clear and damage the paint.
I'd recommend taking it to a body shop.