There is exactly one repeatable double battle in the overworld, that being the match against Shigeki Morimoto and Kazumasa Iwao in the Game Freak office in Heahea City. You can challenge them once per day, and can set up a faster teammate to use a move and then Smeargle Sketches it. Note that Morimoto's lead Gengar has 183 speed and full Special Attack EVs, so you'll either need Smeargle to be faster than that, or at least bulky enough to take a hit so it doesn't get KO'd before it can Sketch.
If getting up to a high enough level that you can use them to sketch one move per day isn't appealing, another thing you can do is use wild Ditto. Delete all moves off of some Pokemon except the one you want to sketch (and it can be low leveled so as not to pose a threat), then search the grass on Mount Hokulani for a Ditto and bring in the Pokemon that only has that move when you find it. Ditto will Transform, then you switch to Smeargle and it uses that move, then you Sketch. In a few cases you'll need a more complicated setup, such as if the move you want to sketch is Explosion.