So, In other words, don't change the cave at all. Not even a little bit. Ideally, you would float down the cave without your feet ever touching the floor, and you would not even disturb the airflow of the tube. Ok, so that's pretty much impossible, but you can do your best. Don't litter!! Don't disturb any bats--if you see any, just leave. Don't touch any mineral formations you see growing anyplace. Don't touch the ice formations. Don't throw rocks. Don't write on the walls with anything. Don't smash anything. "What can I do, then?" you're asking. Well, you can do this to change the caves: pack out any litter you find within them. Report any weird things you see to the rangers at the visitor center (we once found a traffic cone someone had placed in Sentinel!) They may be your caves, but they're mine, too. Don't mess them up! Cave softly!
Instead, head southwest out of the park, stopping by Mammoth Crater, and run on up to Medicine Lake. It's chilly, but it's clean and refreshing for sure! (Summer only, unless you have a snow mobile.)