Chabad.org — English translation + Rashi
Torah Temimah (Pesiqta / related): “על כל בשרם” excludes the hidden places (beit ha-setarim).
English: “And they shall pass a razor over all their flesh” — excluding the hidden places; over the flesh that is exposed.
Gezerah / limitation of “kol basar” — the same language used for immersion is applied to the Levite shaving.
Even a complete purification rite respects the distinction between exposed and private areas; the Torah’s language itself draws the boundary.