does a hand normally can cast spell? no. so your possessed hand can't cast the spell, you have the required training to do so, not the one possessing it, so it won't be able to cast your spell
Spellcasting would need to be called out in Hand's Autonomy in able to function. The feat doesn't state that the hand shares any of its master's spellcasting ability or that it's capable of forming somatic components. I could maybe see a custom upgrade allowing that in a home game, though.