If your going to be regularly testing the real wattage usage of devices with odd wave forms just do what I did years ago and take a stock mechanical KWH meter and rewind the current sensing coils with smaller wire in order to change the rate it reads at. Change it to a 10:1 and you have a KWH with a 1/10 KWH place or do a 100:1 and have a 1/10 and 1/100 KWH places.
Obviously your peak amp limits will be lower due to the smaller wire of course.
Just use a known wattage draw device for checking the calibration after you rewind it and your good to go!
$15 and bit of work and you have a full true reading KWH meter with fine WH resolution. Just run it for an hour and read the actual wattage used.
This is one I built some time ago that I rewound with a 10:1 ratio so it now works as a 0-20 amp, 0 - 240 VAC KWH meter.
I just mounted it in a old external floppy drive case and added lug terminals for the input and output. A power cord and socket would work just fine also.
If I am patient it can show the power being used by a wall power pack.
Just find out how many revolutions per KWH and calculate the time between rotations of the disk to figure out sub watt hour load readings.