As a sidenote, this line on Bulbapedia makes me believe that even more data is stored by the Pokéwalker:
https://bulbapedia.bulbagarden.net/wiki/Pokéwalker#Other_Pok.C3.A9walkers
If this is to be believed, this would imply that the trainer data and entire party for the player is also stored by the Pokéwalker, because the game reconstructs a battleable version of the other player in the Trainer House. I suspect that would imply the Pokéwalker is capable of storing fully formed pkm data, rather than just partial pkm data, since it clearly can store an entire team of 6 from the player party.