Yeah..you would just run one of the source lines from both bats (both pos or both neg)
Make sure you put the switch before the booster in the circuit so that it is not powered up with no load continuously.
I don't know about one switch. You have 2 separate sources coming in to a single contact and then going out to 2 separate boosters. A normal SPST won't know where to send it will it? Wouldn't he be advised to use a DPST switch? I may be wrong, just asking.