They wouldn't be able to carry a paying cargo while Northern ships would be able to carry a paying cargo. This would put foreign ships at a severe disadvantage in the money making business.
I doubt such an arrangement could be made to work long term with other ships not being constrained in such a war.
Be it U.S. ship or foreign ship, once landing the imports in New York or Boston or Philadelphia they would still have to sail empty to a southern port to load up on cotton for the return trip to Europe. Foreign ships because they could not move cargo from one U.S. port to another even if their had been any, U.S. ships because what was there to take to the southern port?