I dont see why you couldnt. Most 9volt batteries test out well above 9 volts brand new so the 9.6 will make no difference. I personally prefer to use Lithium medical grade 9volts as they last 3x as long as a regular 9volt, they also test out at ~11.4 volts new.
ya rechargeables go bad if they sit for long periods of time without being used, i have heard that you can freeze them and then zap them back into life. or at least that what i think i remember reading. i know there are several tutorials if you google it. you could end up with several that work.