Why would a multimeter (ammeter) connected in series prevent the instrumented device from powering on?
What you're doing is fine and correct procedure. Most clamp meters use a current transformer so they only read AC. If you need DC current measurement then you'll need a DC current clamp which will, most likely be based on the Hall effect.
Meters of the 1.999 type are designed with a 199.9 mV full-scale DC meter internally. Every reading is scaled to give 200 mV at full scale on the selected range. That means that a 20 A range will have a resistance of \$ R = \frac {200m}{20} = 10\,\mathrm {m\Omega} \$ so it will hardly affect your drive.
(Note that the shunt may only be rated for 10 A so full scale would be 100 mV. Other meters with, say, 399.9 displays may scale differently, but you get the idea.)