Unfortunately, Keyblades are bit of a necessity in this scenario. At this point in time in-universe, the Keyblade Gliders and Lanes Between are the only known way to travel between worlds since Gummi Ships haven't been invented yet. This means that Non-Bearers are virtually incapable of traversing the worlds. There are the Corridors of Darkness, of course, but those are a bit of a rarity in this setting (Malcolm is thus far the only individual who has ever mastered using them) and I don't think Yen Sid would approve of their use. Plus, I don't think there's much reason for Yen Sid to be teaching pupils who aren't Keyblade Bearers since this does center around a Mark of Mastery exam and all.