Q. I attended an opsherenish for a 3 year old and everyone was invited to cut some of the hair of the child. Do you have to wash your hands after 3 times? (No one seemed to care).
A. Mishna Berura (4: 39) and Oruch Hashulchon (4: 21) write that you only have to wash your hands three times when awakening from sleep or as some stringent Poiskim include, after marital relations and being in contact with the deceased, otherwise once is enough.
Poiskim rule that you have to wash your hands even when cutting someone else's hair (Kaf Hachaim 4: 92) or when cutting only some of the hair (ibid. 4: 68), when using an electric trimmer (Ishei Yisroel 2:41), and even after cutting a child's hair (Nitey Gavriel 15: 1)
However when cutting a small amount of children's hair during the Chalakah tradition many Poiskim rule leniently and you don't have to wash hands (Teshuvos Vehanhogos 2:5, Ishey Yisroel ibid., Piskey Teshuvos 4). A reason given by Mibeis Levy is that you usually do not touch the head, just the hair. Some are stringent and do require netilah (Nitey Gavriel ibid. quoting Belzer Rebbe Zt'l, Piskey Teshuvos 4: 28 quoting Mishne Halocho and Horav Yosef Chaim Zonnenfeld zt"l). The child himself however, should have his hands washed (Nitey Gavriel ibid.)
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a