Install Knoppix to a USB stick, setup a large enough (say, 2-3 GB) persistent store and run.
You never have to access a hard disk with Knoppix, and using USB3 sticks will usually speed up quite a bit also with USB2.
Very often, I run Knoppix on a with no access to the hard disk(s). No problem for me. (Less than top speed isn't a problem for me )