I would use the 9.6 V batteries if you can because not as much power is wasted as heat.
The 7805 efficiency drops off dramatically at higher input voltages.
You probably don't need capacitors if using batteries.
I would look into using switching or 'buck' type regulator instead.
Kind of expensive but you won't need a heat sink and your batteries will last way longer.
Efficiency is nearly the same in relation to the input voltage so higher input voltages don't matter nearly as much.
They also typically have a lower dropout voltage.
Here is one example of a completely self contained 'buck' type switching regulator:
or adjustable version:
Unless specified otherwise my response is based on the latest and fully updated RPiOS Buster w/ Desktop OS.