Mooshimeter does not calculate power consumption, it just stores measured values from both channels to a memory card. Power value you see on the app is calculated live on your phone. But that is not a problem..
For the current clamp situation, you could use one just fine, just select input that matches to your clamp. -10 – +10 amperes between common and amp connectors or -1 to +1 volts between common and “ohm” connectors. DC-clamp does need its own power and the ones with output for external logging are somewhat expensive and/or rare.
But. You could also use existing cabling in your system as a shunt, if there is a single wire that has all the current going through it. You probably need some other way to “calibrate” your setup, so that you actually know how much current there is at different voltage levels over your shunt-wire. Just try to keep that shunt voltage under 1 volt, so that you could use “ohm” connection to measure it.
After finding out a ratio between your shunt current and voltage, you can open your log as a spreadsheet and apply some math to see what you actually wanted to log and graph it for easier evaluation. Or just add the values and divide it by the amount of recorded values in an hour to see watt hours, if you are just interested in the total consumption.