Yes it should be possible since a shiny is determined by the random IVs (hidden pokemon data). It will be the same chance as normal, 1 in 8192.
But you won't be able to tell until you send it back to the game, because the Pokewalker is monochrome.
Sorry Pokemaster, but shininess hasn’t been determined by IVs since Gen 2. I found several sources saying that no, it’s not possible to get a shiny through the Pokéwalker.