We wouldn't just say "have a wash" it's most likely, I wash myself. And yes, it means to clean oneself with water - typically if it was in the bath or shower, we would say "I took a shower/bath". When you say "I washed myself" it most likely means you rinsed yourself off with water.

Have a wash would describe just washing your face and hands. Example 1. I had a wash before I left the house. Example 2. Did you have a wash today