It would be poison. Since he enchanted poison your weapon will be poison even if he has an elemental dagger.
If some is enchant+edp and you have agriope/ed and he notices he can switche weapon, thus enchant will be gone, but edp is still enabled so he is now hitting you either neutral or if he's using an elemental dagger it will be neutral on 1 hand and elemental on the other + edp.