Does Akshan's Weaponmaster keyword, not his ability, allow him to equip an equipment for free?

No, the Weaponmaster keyword does not allow you to equip an Equipment for free.

According to Rule 821.1.b and Rule 821.1.c, Weaponmaster is a play effect that allows you to pay the Equipment's Equip cost, reduced by [A] (a power of any domain), to attach it to the unit with the Weaponmaster keyword.

It does not make the equip cost zero; it simply provides a discount of [A] to the cost of the Equip ability. If the Equipment's Equip cost does not contain [A], you must still pay the full cost.