My recommendation is to try to hit as many trees as possible at the ground level rather than trying to get nuts from high up on a single tree.
Nut pickers work pretty well for harvesting in the when the nuts are preparing to fall when they are ripe, but right now they hold on to the tree pretty hard, and you can do a good amount of damage to the branches trying to pull them off.
If you can actually reach by hand, you can twist them off without much trouble.