Some general tips in matchup.
Priority for summons are Dog > Ghost > Raoh > naked > Sword. Sword is completely useless in the matchup, so manage the clock to get dog or ghost, if you get sword on wakeup you're fucked. Naked lets you spit and centipede so its > sword in the match. Never raw summon if the clock is set to give you sword.
Dog allows you to still attack while blocking Eddie mixup and Eddie has no way of dealing with dog pressure and corner unblockable setups. While you have ghost active the matchup is heavily in Zappa's favor. Eddie has to run the obstacle course to try and land a hit since summoning against ghost is difficult. As good as Raoh is Eddie is still better so don't always go for Raoh unless you get a confirm into Centipede.
Go into training mode and learn to Instant Block the second hit of Mawaru (Shadow K release) and back dash out. If I'm not mistaken Zappa's back dash is really good. You can also try to slash back it + throw > centipede > back dash. That takes a lot of practice though, so the IB back dash might be easier.
While Shadow gauge is cooling down that's the time to really go in with Dog and setup bite.