Lincoln had already been advised by his Military experts that it would take a force of 20,000 men to reinforce that fortress. A token force of 1,400 could serve no other purpose than a provocation.
It could not take the Fort, it could not serve as an effective attack, it literally served no other purpose than being a pawn move in an opening game.
Like President Buchanan before him, Lincoln was not willing to surrender Fort Sumter, unless he could achieve something major for it, such as "a fort for a state", Virginia.
The force Gustavus Fox requested was intended to go in & out, assuming no opposition or only minor opposition.
It was not intended to conquer all of Charleston, which as you say was estimated to take 20,000+ troops.
Lincoln attempted to insure Fox's success by offering Governor Pickens no reinforcements if there was no opposition.
But Pickens didn't care a whit for Lincoln's offer, nor did Jefferson Davis.
In the end, the force which arrived at Charleston harbor the morning of April 12, 1861 consisted of only two ships -- the revenue cutter USS Harriot Lane, crew of 95, and the civilian steamer SS Baltic with supplies and about 200 troops.
But it didn't matter.
The Confederacy had long before decided to go to war, and this was as good an excuse for them as any.