My 3yr old son has recently developed this liking to guns and shooting games. We don't have toy guns at home but he will pretend with his hand and pretend to shoot people. Is it okay?

This is a very debatable topic. There are studies which contradict both the arguments: 1. letting children play with guns and 2. not allowing them to play with guns. I would say you son is just 3 years old. Let him play with what he wants but do give him instructions and advices like you shouldnt point the gun at another person, etc