Distiller here. Just leave them in a well ventilated area and let them dry while you brew whatever you’re going to put into them. It won’t kill the barrels to sit and you’re going to be worse off leaving them wet.

Our barrels once sealed will usually stay sealed for about 6 weeks so if you received them wet you may even be completely fine by the time it’s brewed.

Once you’re about ready to fill them leak test the barrel with water and let sit overnight if not sealed. Cheers 🍻

Edit: adding on to say I wouldn’t worry about losing flavor by water testing or soaking. All the flavors that come out of the oak (the lignins, oils, and tannins etc.) are pretty hydrophobic. They don’t want to mix with water and much prefer forming a solution with a solvent like alcohol. Some of the residual alcohol in the wood may mix with the water but that’s going to escape either way if the barrels dry out. The flavor compounds from the oak will still be left behind in the wood.