I believe this is probably "In Case of Fire" (1960) by Randall Garrett; first published in Astounding, it was anthologised by Greenberg-Waugh in 101 Science Fiction Stories. It is available to read at Project Gutenberg.
It matches all the points listed, including the 3-day timeline, the team of a paranoiac and someone incapable of deciding between options and the ambassador himself being an agoraphobic xenophobe.
Earth is at war with an alien empire, evenly matched.
Somewhere out there, a war was raging. He didn't even like to think of that, but it was necessary to keep it in mind. Somewhere out there, the ships of Earth were ranged against the ships of the alien Karna in the most important war that Mankind had yet fought.
There are other alien races, but they are sitting on the sidelines.
The sort of grandstanding the Karna were putting on had to be played to an audience. But there were other intelligent races throughout the galaxy, most of whom had remained as neutral as possible during the Earth-Karn war.
The aliens request a peace treaty with Earth, but in 3 days at a place far from Earth. The goal is to force the Earth to lose face by failing to negotiate.
They had sent a full delegation to Saarkkad V, the next planet out from the Saarkkad sun, a chilly world inhabited only by low-intelligence animals. The Karna considered this to be fully neutral territory, and Earth couldn't argue the point very well. In addition, they demanded that the conference begin in three days, Terrestrial time.
Earth has a small diplomatic outpost nearby, of mostly diplomatic outcasts. They ask the director to send a negotiation team.
But Malloy didn't have top-grade men. They couldn't be spared from work that required their total capacity. It's inefficient to waste a man on a job that he can do without half trying where there are more important jobs that will tax his full output.
So Malloy was stuck with the culls. Not the worst ones, of course; there were places in the galaxy that were less important than Saarkkad to the war effort. Malloy knew that, no matter what was wrong with a man, as long as he had the mental ability to dress himself and get himself to work, useful work could be found for him.
The director sends two diplomats, one who is unable to make up his mind unless convinced there is only one correct path. The other sees conspiracies everywhere.
"Nordon had a mental block against making decisions. If he took a girl out on a date, he'd have trouble making up his mind whether to kiss her or not until she made up his mind for him, one way or the other. He's that kind of guy. Until he's presented with one, single, clear decision which admits of no alternatives, he can't move at all.
"As you can see, the Karna tried to give us several choices on each point, and they were all rigged. Until they backed down to a single point and proved that it wasn't rigged, Nordon couldn't possibly make up his mind. I drummed into him how important this was, and the more importance there is attached to his decisions, the more incapable he becomes of making them."
The Secretary nodded slowly. "What about Braynek?"
"Paranoid," said Malloy. "He thinks everyone is plotting against him. In this case, that's all to the good because the Karna are plotting against him. No matter what they put forth, Braynek is convinced that there's a trap in it somewhere, and he digs to find out what the trap is. Even if there isn't a trap, the Karna can't satisfy Braynek, because he's convinced that there has to be—somewhere. As a result, all his advice to Nordon, and all his questioning on the wildest possibilities, just serves to keep Nordon from getting unconfused.
This combination stalls the alien negotiators, by forcing all terms to be explained in depth with no possibility of trickery.
By the time the ship from Earth got there, the peace conference had been going on for four days.
When relief finally arrives, they ask the director why he didn't go himself. The director explains that he is a xenophobe.
The Secretary of State raised an eyebrow. "Couldn't go, Mr. Ambassador?"
Malloy looked at him. "Didn't you know? I wondered why you appointed me, in the first place. No, I couldn't go. The reason why I'm here, cooped up in this office, hiding from the Saarkkada the way a good Saarkkadic bigshot should, is because I like it that way. I suffer from agoraphobia and xenophobia."