Little things can make a big difference in your aikido if you choose things that affect every single part of aikido. This is why basic exercises like tegatana andhanasu have so much leverage to improve your aikido. Anything that you improve in these ends up improving all the rest of your aikido in small ways, until all those small improvements snowball and make a big difference.
One little tidbit that will help in hanasu is the positioning of tori's hand as he offers it for uke to grab. Tori wants to make sure that he presents the arm low, close to his own body, so that tori's face and hand are both the same distance from uke's lead shoulder. What this does is makes it unclear to tori's subconscious whether the attack is coming to the face or the wrist. Tori is helping uke to make a stronger attack and this forces tori to learn a response that begins as uke crosses maai and is viable for either attack. This also goes a long way toward tying all the wrist stuff (hanasu) together with the striking stuff (nijusan) so that we are not doing tegatana, then stopping that and doing a different thing (hanasu) then stopping that and doing something else (nijusan), etc... We're working on different views or facets of the same thing (aiki) throughout class. So, with hanasu, low is the way to go.