An alternate before trying shaving would be to wipe down with Sea Breeze (all the bits and your crack) after you shower. I had a really bad case of jock itch in college and part of the cure per my doctor (in addition to a strong topical fungicide) was using the Sea Breeze. After over the years finding that I am prone to jock itch, I have used Sea Breeze routinely. It seems to prevent any rashiness, include the pimples that can be common in that moist area.

The problem with shaving is that it can make you rashy by itself, as well as causing in-grown hairs and chafing from the stubble if you then stop shaving.