In order to perform Edo Tensei you need a host. While Kabuto illustrated how Edo Tensei is performed to Tobi, you must have noticed that Kabuto used a host for it.
Once the ET is successful, the body will retain the properties of Edo Tensei jutsu, i.e. the body cannot be destroyed (for instance, if the body is cut or if it was pierced, it would wrap itself with tiny bits of paper, it cannot be felt by the reanimated souls).
But the host (which is present inside ET's body) does contain blood. With help of that, any person under the influence of ET can perform Kuchiyose no Jutsu. Don't forget that Edo Tensei is a Summoning Technique in itself.
Mizukage is a high level shinobi, so he doesn't need to perform any handseals.
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