No, it wouldn't work, because Darkrai is your Pokemon.
Sketch allows the user to copy the opponent's last move permanently, therefore replacing Sketch.
Only if you are facing the Darkrai can you sketch its last move.
If you really want a move that puts your opponent to sleep, give your Smeargle a Chesto/ Lum Berry and sketch something with Spore or Sleep Powder.
Bulbapedia - Sketch