From what I understand, you have to wear a chute unless it is specifically for the training requirement of the cfi certificate. I used to teach aerobatics while I was in college and I think its smart to go ahead and wear a parachute anytime you are doin abnormal maneuvers such as this. In addition, when I would give a cfi applicant spin training, I would take them do some basic aerobatic maneuvers as well. In my opinion, having some knowledge of basic aerobatics makes someone a better pilot anyway. I would go to an aerobatic school for your spin training, generally those instructors will be better, you will have a chute on and you may get to see some other maneuvers too.