Not a problem. After a few uses, voltage will drop a bit anyway. All electronic devices can operate on a certain voltage range, because batteries range a lot depending on the charge. One full volt over or under is not a problem. My Zoom F8 recorder can operate reliably on anywhere from 10 volts to 13 volts.
I'm sure you will be fine, as the other poster has said battery voltages vary and I would guess that there is a voltage regulator in the camera anyhow.
p.s. throw a link up of this battery, my a6300 eats through its batteries I might buy a few myself (assuming the a6300 and a6500 use identical batteries).
There is no physical difference between the 2. All DV size Li-Ion batteries are 8.4V when fully charged, and just around 6V when discharged. While being discharged in the camera, they cross ~7.2V about a midpoint. Some manufacturers call 7.4V a midpoint, others feel like 7.2V is the magic point. It is just what they write on the battery label, there is no direct relation to how a Li-Ion battery works.