Power just the Arduino-related part of the circuit with the 9V-to-7805.
Power the servos, separately, with the 6V pack. 6V is pushing the envelope, but I think you'll be OK.
[Remember, connect the Grounds together...] OK?
I think a hand is too much. No servo of the hobby sort is going to push your hand out of the way no matter what battery it's connected to.
Some of this stuff you just have to experience out like.
You could get a big 12V sealed lead-acid (SLA) battery for big-time current.
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