" Captain Waddell, the commander of the Shenandoah, states that the last vessel he spoke to was the Barracouta, of Liverpool, bound for San Francisco. He met this vessel at sea on 3rd of August, and leamed from the captain that the cause of the South was irretnevably lost. Captain Waddell, on hearing this news, expressed his intention to proceed to England, and arrived off this port yesterday morning. He then took a pilot on board, and, fmding the intelligence he had received from the captain of the Barracouta as to the subjugation of the South undoubted, he desired the pilot to take his ship alongside one of her Majesty's vessels of war, if there were any in port. The Shenandoah was taken up the river at high water, and, according to the instruction given to the pilot, she was moored alongside the Donegal. A crew from that vessel was placed on board her, and the customs authorities having been communicated with, some officers belonging to that department were also placed in charge. Soon after the surrender of the vessel, Captain Waddell and several of his officers and crew went on shore." - Liverpool Mercury, Nov 7th, 1865
"I have, therefore, sought this port as a suitable one "to learn the news," and, if I am without a Government, to surrender the ship, with her battery, small arms, stores, tackle, and apparel complete to Her Majesty’s Government, for such disposition as in its wisdom should be deemed proper." - Capt. Waddell of the Shenandoah surrendering his ship to Earl Russell, Nov. 5, 1865
Sounds like a surrender to me.
Captain Waddell took her to England, arriving in Liverpool on November 6, 1865 where he turned the ship over to British authorities.
"[A]bout 6 o`clock last night a telegram was received from Government by Captain Paynter, of her Majesty’s ship Donegal, to whom the Shenandoah was surrendered" - Liverpool Mercury, Nov 9th, 1865
Sounds as if he surrendered to to one of their naval vessles.
The crew was paroled by the British government and were never in U.S. custody at any time.
It appears that they were paroled onto shore in Liverpool, though I cannot find what happened to any of them upon return to America. Waddell did intend that his surrender to the British would result in the ship's placement into United States custody:
"I think that as all the property of the Confederate Government has reverted, by the fortune of war, to the Government of the United States of North America, therefore this vessel, inasmuch as it was the property of the Confederate States, should accompany other property already reverted." - Waddell's surrender letter to Russell, Nov. 5, 1865