Actually, I wish to respectfully disagree with this statement. Bushwhackers/Guerrillas usually operated for either side. They were usually the radical edges of either side, not wholly military, and not wholly untrained militarily.
When someone says, "Third Party" to me, I get the impression of the Hessians used by Britain during the American Revolutionary War. Paid mercenaries actively engaged in the conflict.
For all my reading and research, I have never found where any other country was actively employed by either side, or provided troops as a paid service to either aggressor.
The closest I've come to this would be the use of blockade runners to transport goods into and out of the Southern states. The reasons behind it would be instant wealth, and the need for certain goods required. In this case, the operators of the blockade runners were mostly British.