>>1Not safer.
You can get a disease just for peeing on a public bathroom. Some people are nasty.
I saw a video some time ago of a hidden cam on a public toilet and it was disgusting. Most women wouldn't clean their cunts or hands and many excreted dark fluids (maybe from menstruation?) that was outright nasty. Penis is better. No contact with the toilet and no need to wipe after pissing. Much safer.