Where's that power from? The compendium does not know it. I only found garrote strangle, but there's nothing like "light blade" in it.
Yes, the secondary attack is described in the flavor text as a punch with a fist, and the base damage is expressed as 1d6 instead of some number of [W]s, but nothing in the power implies that it loses the weapon keyword.
This means that any benefit that you get for using a weapon keyword power should apply, including adding your magic weapon's enhancement bonus to the attack roll and damage roll, bonus damage on a critical hit, other applicable magic weapon properties, and extra [W] damage on a crit if you are using a high crit weapon.
If this bothers you, you could house-rule the power to make the flavor fit more closely with the mechanics.
There is nothing in the rules that says this, and the clarification on weapon damage rolls does not mean that the attack does not count as a weapon attack. There are other weapon attack powers without a [W] damage roll (off the top of my head: Knockdown Assault). That doesn't mean anything for the power itself, which still gets your main weapon's enhancement and proficiency bonuses, and any properties will apply, along with any extra damage should you crit.Fine but the weapon keyword also includes unarmed attacks. A fist is a weapon.
From the Compendium
Roll the damage indicated in the power description. If you’re using a weapon for the attack, the damage is some multiple of your weapon damage dice.
As this isn't [W] you aren't using a weapon in the traditional sense, you are most likely using your fist.
My guess is that you copy-pasted my spelling in, which is incorrect. It's in the PHB, 15th level rogue daily, and it shows up in the compendium for me.
Irregardless the point is that it's a power which grabs your target, strangles them to unconsciousness and uses them as a body shield, and it absolutely cannot be performed without wielding a light blade. Actually a lot of rogue powers are like that: think you can perform knockout with a sap? Nope: you knock people out by stabbing them, thank you.