[KevinJ]

Historically...

Light Infantry (missile weapons) defeats Other Infantry (melee) because the Melee has to close the gap under fire. Once Other Infantry closes to Shock action, the light infantry is toast.

Setting aside the Wight bit.
In an open arena the unarmored Fencer will loose because he has no cover or concealment to exploit as he closes the gap. Heavy Infantry at least has armor and shield and mutual protection from missiles, but while advancing they become targets for flanking, usually by cavalry.

If being a Wight isn't good enough, add increased maneuverability and speed to that the Fencer can outrun the blocker, using the Defend option to become harder to hit with missiles or use a gimmick (smoke bombs, etc.) to obscure the view of the light infantry to that the fencer can destroy the blocker before moving in on the light infantry.