I think the power consumption and current requirements of the pump
will be the determining factor for the battery size.
A23 sound like a button size format, so maybe suitable for the sender.
What module is "the module" you are talking about?
The 433/866MHz modules are often operated from 12V on the receiver side.
To select a suitable battery/accumulator, you have to provide a lot more information,
about the pump, the wireless module you want to use,
the temperature range, ...
Keep in mind that I'm not a low-power or power supply specialist, by any means.