I'll take a stab at this... note that when I write "Greek" I mean classical Greek, not Bronze Age Myceneans, for instance.
Dagger - both
Mace, stone headed - Egyptian
Sickle - both, I think
Club - both
Flail - Egyptian
Mace, bronze headed - Egyptian
Shortspear (Short Thrusting Spear) - both
Crook - I've never heard of this being used in Greek myth, but I suppose it could be both... it basically seems just like a club. Both?
Longspear - This gets a bit complicated. Before the Athenian mercenary Iphicrates' reforms around 400BC, hoplites used spears between 6' and 10' long (according to Warry). I don't think that merits reach. Iphicrates' men used a 12' spear, which I guess could have reach. I don't know if the Egyptians used this.
Spear - both
Staff - both
Sharpened Stake - both
Dart - unsure. I haven't heard of either using them although I think they were used by some Bronze Age civilizations, maybe the Myceneans...
Javelin - both
Javelin, Mycenean - Well, Myceneans However I read just recently in John Warry's good book on classical warfare that Greek javelins used a throwing loop too.
Rock - both
Sling - both
Throwing axe - Egyptian
Hammer - Egyptian, unless your Greek blacksmith has to pick one up in a pinch
Hand axe, cutting, piercing - Egyptian
Net - both, but I don't think either made much use of them as weapons
Whip - both (ditto)
Sword, short stabbing:
- Cretan stabbing, Kopis, Xiphos are Greek
- Khopesh is Egyptian
- Akinakes is Persian, as noted in the book
Trident - Greek, I guess
Greatclub - both? certainly Greek
Labrys - err, well, Greek/Minoan I suppose (I think it's silly)
Sarissa - Macedonian...
- Horn and Self Bows - both
- Composite Self Bow - both
- Composite Recurve Bow - Egyptian
However, mainland Greeks used bows very little in warfare, although the Cretans were famed for it; in classical times the Athenians used Scythian mercenaries, and Cretan archers were available as mercenaries in the 4th century. The people of Rhodes were famous as slingers around 400BC when Xenophon and the army he was in signed on with Cyrus (and had to fight their way out of the Persian empire)