If it needs an 11mm hex key that's what it needs. Usually when a freehub becomes less free it's because either thick grease buildup, and/or dirt binding the mechanism. Obviously remove the cassette from the body, then remove the body from the hub, and give it a long soak in mineral spirits.

Once it's soaked a while see if it can be worked free in your hands. If so keep working it and rinsing until it's free and the rinse solvent runs clear. If it comes back to life, it needs to be shaken free of excess solvent, dried in a warm place, and re-lubricated using a heavy oil such as Phil Tenacious or this other chain lube which I won't mention but the label looks like a perfume label.

Some freehubs have an oil port in the splined area, others require that you work it in past the bearing clearance. If you have one without a oil port, it helps the oil flow in faster if you warm both the freehub and oil. Don't get carried away, about 125-130 (the temperature of hot tap water) is plenty.