Question

Not cheats

Answer 1

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.

Comments

I guess you might as well catch every pokemon you find on the Pokewalker then...