As far as I can tell, the differing PIDs depending on TID and SID ensure that the Pokéwalker Pokémon can never be shiny.
A Pokémon is shiny if its TID, SID, and both 16-bit halves of its PID XOR together to make a number less than 8.
For all the Pokémon of PIDs with the format 0xXX0000YY, the XX is the inverse of the upper 8 bits of TID^SID. Therefore, the 'shiny value' for these Pokémon takes the form of 0xFFZZ, meaning that they can never be shiny.
For the Pokémon with PIDs like 0xXXFFFFYY, the 'shiny value' differs; however, the lower 2 bits are always 1 in the samples above.
The 'shiny values' for the given Pokémon are (in the same order as above):
0x0304
0x0301
0xFF98
0xFF4F
0x03DB
0xFF37
0xFFE8
0x0FCA
0x1FC7
0x039A
0xFF0F
0x7F9D
So it looks like Pokéwalker Pokémon can't be shiny. I'll test this theory with my Pokéwalker-obtained Pokémon, too. However, we still need to figure out what determines which of the two groups a Pokémon falls into (0xXX0000YY or 0xXXFFFFYY). Could you provide the gender of each of the Pikachu?