I hope they're suitably impressive looking units. You don't send your Secretary of state to negotiate a treaty in a VW bug! (Nothing agaisnt VW bugs, they're fine cars, but they ain't Limos).
Envoy cruisers should be capable ships outside of their special abilities, just expensive to build so you don't load your fleets with them. I would like them to be just a step down from Capital ships in terms of size and combat capability.
And you do send your capital ships to negotiate treaties in the real world, at least historically. If it's to a nation that you just won a war against, then it's to reinforce that fact, and if it's to a nation that you're allying with, then it's to impress them with your value as an ally. Historical actions by ships isn't typically a major concern, as it's the commander of such ships that bear the glory or infamy of it's actions in most cases.