Hi Josh
,
IMHO not a throwing weapon, as you said all edges are sharp, not conducive to be held and thrown by hand, a large sling shot would be cut to pieces in a very short time too. Ovoid, round and spherical missiles tended to be the norm, more aerodymanic etc.
I have a suggestion perhaps these were grave or votive offerings. Stone age man had sophisticated beliefs in the after-life. Perhaps, the sharp edge all away round insures that 'mortal' man would not be able to use it ....but the spirit ancestor could. If this type of axe head was bound to a shaft , the edge would cut the bindings and if used as a hand axe, the palm and fingers would be lacerated. Perhaps suggesting it's use could only be by an 'unworldly' being.
All the best
David