Along with queensaki, a user on YouTube by the name of ITP123 has posted a number of videos of the Japanese retail demo of Brawl. Several of them feature Ike, King Dedede, and Pokémon Trainer, but one in particular is interesting in that it shows how exactly Pokémon Trainer can select the first Pokémon that appears:

It should be noted that Pokémon automatically switch out whenever one is KO'd, and a look at Super Sudden Death suggests that a switch out happens then too.