An electrical shaver particularly useful for wet shaving includes a manually-grippable housing, and a cutter head removably attachable thereto along the outer edge of the cutter head. The cutter head includes at least one relatively sharp scraper edge located between the outer side of at least one cutter unit and the outer edge of the cutter head, but does not extend to the inner side of the cutter unit facing an adjacent cutter unit, such that the scraper edge is pressable into the skin, forwardly of the respective cutter unit, to erect hairs in the skin and to tauten the skin in advance of the respective cutter unit, with minimal irritation of the skin, as the cutter head is moved across the skin in the direction from the outer side towards the inner side of the respective cutter unit.