Sigrok runs on Linux, so you'll need a SBC to run the OS where you install Sigrok. I doubt there is any SBC that can run hundreds of hours from a pair of AAs. The state of the art in low-power single board computer these days is the mobile phone. Mobile phones have bigger batteries, yet they still don't run for that many hours.
So, either you port Sigrok to a bare-metal microcontroller (which might be too complicated in terms of software), or use any casual SBC board, but with an external power source, such that the end user can power the device either from a PC USB port, or from a USB phone charger, or from a beefy USB Li-Ion power bank.
You might also add an internal socket for a 18650 Li-Ion battery (accessible from outside), so the end user can insert the battery without dismantling the unit, and you won't have to deal with Li-Ion shipping regulations.