In accordance with one aspect of the invention there is provided a shaving unit (10) that comprises at least one blade (20, 24) and a skin engaging member (64) that has a surface (74) for engaging the user's skin adjacent the blade edge. The shaving unit may be of a disposable cartridge type adapted for coupling to and uncoupling from a razor handle or may be integral with a handle so that the complete razor is discarded as a unit when the blade or blades become dulled. The blade edge (or edges) cooperate with skin engaging surfaces to define structure having a desired geometry. The skin engaging member (64) is comprised of an elongated sheath (72) made of a mixture of water insoluble matrix material and an effective amount of shaving aid material and rigid core (70) material extending axially throughout said sheath (72). The axial position of the core (70) need not be through the central axis.
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