I didn't get to go to a morgue but did go to a funeral home, a cardiac rehab and dialysis center. One class even went to a exhibit called Body Worlds... http://www.bodyworlds.com/en/pages/home.asp
Fake it till you make it worked for me. No matter how freaked out I felt, I just never let them see it. Pretend to be calm and confident....heck, I still do it and no one can tell! Good luck!