I'd say that dsteg has pretty much summed things up.
A nephew of mine had the same issue when he was very young. He had a howitzer of an arm and getting hit with the ole horsehide wasn't fun. He developed this cautious demeanor which was admirable, but every other batter he faced soon crowded the plate.
My brother in law did exactly what dsteg suggested. The first time my brother in law got dinged, my brother in law hit the ground, started flopping around like a fish out of water, started to ball his head off, paddle his legs, rolled in the clay, and then got back up dusted himself off and with a deadpanned look told my nephew ... " go ahead, hit me again..."
The kid started to get over the situation, and they both had a good laugh. Before the day was over, no more apprehension about hitting the batter.
However ... I did got out of my lawn chair and asked my nephew not to hit his dad too hard ... he still had my lawnmower!