A 9V alkaline battery will measure ~ 9.5V when new.
A 8.4V (nominal) rechargeable NiMH battery will measure ~9-10V (and peak at 10.5V) when fully charged, depending on manufacturer.
A 9.6V (nominal) rechargeable NiMH battery will measure ~10.5-11V (and peak at 12V) when fully charged, depending on manufacturer.
You'd have to know the exact voltage regulator on the board to see if they can handle the 11 or 12 volts coming out of a rechargeable.
I guess the whole reason I'm asking is cause I have a virtue board for my shocker and I have stinger grips. With a regular Duracell battery the grips will have a gap between them and the frame puting pressure on the oled screen which could break it. I've tried a rechargeable battery and it fits good cause the battery is a little thinner. But I haven't tried a alkaline battery yet.