Do the obvious.
Give the wedge and the metal around it a good dose of penetrating oil and let it sit for a day or so.
Then, support the left side of the barrel with a couple of blocks of wood with the large end of the wedge hanging down between them.
Use a piece of brass or aluminum and a 2 pound hammer and give the exposed upper end of the wedge a good stout whack.
As long as the left side of the barrel is supported by the wood and your using a brass or aluminum piece to transfer the hammer blow to the wedge, you won't damage anything.
Because the wedge may release at any time when you give it a blow, I strongly advise that you hold the brass or aluminum piece with a pair of pliers.
Given enough persuasion, the wedge will eventually release its grip on the barrel arbor and the sides of the barrel slot.
The marks left on the wedge by the brass or aluminum block can be removed with a little oil and some steel wool.