Emissary of Grudges vs. Annihilator
No, there is no interaction. Emissary of Grudges can change a target, but the Annihilator ability does not target.

"Target" has a specific meaning in Magic. If an ability does not specifically include the word "target" somewhere, then there is no target for Emissary to change.


  115.10a Just because an object or player is being affected by a spell or ability doesn’t make that object or player a target of that spell or ability. Unless that object or player is identified by the word “target” in the text of that spell or ability, or the rule for that keyword ability, it’s not a target.


Annihilator does not target anything:


  702.85a Annihilator is a triggered ability. “Annihilator N” means “Whenever this creature attacks, defending player sacrifices N permanents.”