Armed force actually began on December 26, 1860 when Federal troops overpowered a ship's captain (he fought back at this piracy) and had him take them to Sumter, and when they arrived at Sumter Federal troops charged the civilian laborers there with bayonets.
The ship incident is described in E. Milby Burton's excellent book, The Siege of Charleston, 1861-1865."
You'll notice Davis said "Armed insurrection began ..." and there's good reason for that. If a police officer commandeers a vehicle to chase fugitives it's not a casus belli. If state officials start attacking federal troops, it's going to have serious repercussions.
I've got David Detzer's Allegiance: Fort Sumter, Charleston, and the Beginning of the Civil War in front of me. He describes the transfer but I can't find your incident, unless you mean this: "The skipper of the rented schooners sensed what the signal meant and tried to prevent Hall from taking the boats to Sumter, but Hall and a sergeant shoved the captain into the hold and took off, arriving shortly after Seymour."
So they rented a boat, and used others of their own, and the captain balked when he found out what they were doing. More broken agreements from the South Carolinians.
The South Carolinians verbally explained that any shift of troops by Anderson from Fort Moultrie to Fort Sumter would violate their proposal. Buchanan said that his policy was to maintain the status quo but that he couldn't pledge anything. He said that it was a "matter of honor among gentlemen."
From Klein: "All parties went away believing a bargain had been struck, without knowing exactly what the bargain was, who the parties to it were, and what its precise terms were."
"Informal truce" indeed! It's a fine agreement when no one knows what they're agreeing to? Buchanan says he can't pledge anything, and they assume he's promised them something?
There's something more than a bit surreal about Congressmen demanding that the President acquiesce in the seizure of American military installations. Detzer notes Buchanan's long diplomatic experience, something the militants should have taken into account.
I don't think this discussion is going anywhere. The idea that state officials could declare themselves independent and start giving ultimatums to the federal government overnight is so far from experience and understanding that it's hard to take it seriously.