Okay I figured some more egg move Pokemon out:
Custom Shiny Egg Moves:
Snorlax: Fissure, Charm, and Double-Edge
Sneasel: Double Hit, Ice Punch, and Crush Claw
Horsea: Disable, Dragon Rage, and Signal Beam
Skorupi: Agility, Faint Attack, and Slash
Non-Custom Shiny Egg Moves:
Paras with Cross Poison and Bug Bite
Ekans with Fire Fang, Ice Fang, Poison Fang and Thunder Fang
Machop with Fire Punch, Ice Punch and Thunder Punch
Poochyena with Fire Fang, Ice Fang, Poison Fang and Thunder Fang
Custom Shiny Egg Moves:
Snorlax: Fissure, Charm, and Double-Edge
Sneasel: Double Hit, Ice Punch, and Crush Claw
Horsea: Disable, Dragon Rage, and Signal Beam
Skorupi: Agility, Faint Attack, and Slash
Non-Custom Shiny Egg Moves:
Paras with Cross Poison and Bug Bite
Ekans with Fire Fang, Ice Fang, Poison Fang and Thunder Fang
Machop with Fire Punch, Ice Punch and Thunder Punch
Poochyena with Fire Fang, Ice Fang, Poison Fang and Thunder Fang