You can sense it:
Axe is 1h while Greataxe is 2h.
Sword is 1h while Greatsword is 2h.
Mace is 1h while Warhammer is 2h
Staffs are 2h while Catalyst is 1h (off-hand)
Daggers 1h
Guns 1h while Bows are 2h

I think thats all.

Only mild correction. Battle axe is the 2h, everything else is spot on. There's a few Battle axes, the great axe and the executioner axe, Just nitpicking tho :D

Although I would prefer to have the accurate description...I didn't sense it personally, I ended up guessing, since one "tends" to have more damage then the other. but there's no way of telling outside of that, so yeah, getting the 1h / 2h moniker will be nice.

Well there could be 3 solutions I can think of
1. Implement single/2 handed description /best one/

The below solutions would help only if you could equip the weapon....so dropping weapon that you don't meet requirements for at the time would still be uncertain.
2. on equip the other field would uneqip
3. If 2 handed both hands field shows the weapon image