Big bump because, while this thread may have been inactive for a long time, I've been using it to look for some Puppets that I might consider for my team. However, I believe that the list is incomplete, as I've found a few additional Puppets that can use certain useful moves:
Stealth Trap:
Defense Sara
Power Tenshi
Assist Tewi
Power Hatate
Bind Trap:
Assist Parsee
Assist Tewi
Chasing Attack:
Power Suika
Speed Meira
I'd also like to recommend a few Puppets that can learn the following additional useful moves:
Phase Inversion (Reverses all of the opponent's stat changes. +1 Priority. Useful for revenge-killers?):
Power Yumemi
Speed Yumemi
Normal Seija
Defense Seija
Speed Seija
Normal Miko
Power Miko
Speed Miko
Speed Utsuho
Wind God Protection (Doubles the Speed of the user, and all the user's allies for 4 turns. Basically, it's Tailwind.):
Assist Tokiko
Speed Aya
Assist Hatate
Power Kanako
Defense Kanako
Power Sanae