The time you spend in the cadaver lab is minimal at Case. I'm in my first year and I've only been in there roughly an hour at this point with maybe another hour to go...so not too bad. As Dr. Rex stated, everything is already prosected and the instructors point out the important parts, you are not required to touch anything if you don't want to.
I wouldn't lose any sleep over the anatomy lab, it's not a big deal at all. Good luck to ya!