Based on my past experiences as someone who walked home on the beach just after sunrise almost every morning i would say it is one of the safer times and a time when you get hassled less. I am not the all night partier i once was but i had a few really late nights last april and walked home on the beach shortly after sunrise and times may have changed but all i usually saw on the beach at that time were joggers, people looking for shells and people raking the beach. Its light out and hotel security people are visible and you wont be the only tourist on the beach so i wouldnt let fear keep you from enjoying your early morning walks. As with any time of day in Negril or anywhere else in the world for that matter just be aware of your surroundings and use common sence and you should be just fine and most importantly enjoy your time in Negril