To be fair the jet propelled weapon can still be attached to a war axe to give the same effect. Big swing, burst of extra propulsion, deeper hole in the target.
And it doesn’t have to effect the size either. A small jet engine can be built into the head of a one-handed axe.
you could also try and build another small engine into the handle of the axe so that it can levitate, then have the axe fly back to the owner if thrown. All using jet engines.