I am using a safety razor for my head. Once every 2-3 shaves I cut myself (usually on my non-handed side) but otherwise no issues. The cut usually heals by the time I'm done and I have rather thin/sensitive skin.

Derby or Feather blades and a cheap €15 handle. I try to shave once with the grain, once sideways. The blade is held at quite am angle but with very little pressure.