Yes, the railings are at waist height pretty much everywhere that it is possible to go in the main cavern. Waist height is not necessarily ideal for every shot, but you should be able to make it work. It would definitely be better than my mini-tripod where most of the time my only option was to set it on the floor, which had the limitations of 1) having to get down on hands and knees to set up the shot (although this is a limitation due to my old DSLR; with yours, you will be able to view the screen without having to put your eye in the eyepiece); and 2) A lot of the view is blocked from the floor, either by railings or by cave features on the ground that stick up a few feet in height.
You can see from CrackRabbit's photos how the tripod (and the accompanying proper technique such as using the timer to eliminate vibrations) makes a huge difference. He was able to use lower ISO's, longer shutter speeds, and smaller apertures; all of which improve the image quality. So a relatively cheap yet high quality P&S (I had the DMC-FZ20, and I gave a DMC-FZ3 to my parents, so I like that line of cameras) can get great results with a tripod, compared with my $1500 lens+camera without a tripod.
So I would definitely take either the clamp or the full-sized tripod. The full-sized tripod will give you more flexibility, but the clamp would certainly be a lot smaller, and you should be able to find a place to clamp it almost everywhere.