I always recommend walking away from the privy.
This was at the Morgan Stewart Memorial shelter on the Appalachian Trail in New York, just a few miles away from busy I-84. It was my first time at a trail shelter, and I enjoyed hearing other hikers’ stories from their months (yeah, months) on the trail. We met two women who were each hiking all 2,190 miles of the trail alone and happened to stop at the same shelter for the night. They had both made keeping extensive journals part of their nightly routine, and they would send the notebooks or loose leaf pages home to their families along the way.
Although a privy might sound like a luxury worth taking advantage of, trust me. Taking care of business in the fresh air sans toilet is much more pleasant than sitting anywhere near a privy.