.
I knew I had remembered reading of what was reported as the last neutral ship to leave Finland somewhere, found it on DANFS*
...
American Legion departed New York City early in February 1940, on her maiden voyage, bound for Panama. Over the next few months, the ship made five round-trip voyages to the Canal Zone, with stops at Charleston, S.C., and San Juan, Puerto Rico, carrying civilian and military passengers. The worsening situation in Europe, though, soon resulted in the ship's receiving a special mission.
President Franklin D. Roosevelt directed that American Legion leave New York immediately and proceed to Petsamo, Finland. There, she was to embark the Crown Princess Martha of Norway, and her party, to bring them to the United States, their homeland having fallen to the Germans the previous spring. Further, as Acting Secretary of State Sumner Welles reported to the United States Minister in Sweden, the President also desired that Mrs. J. Borden Harriman, the former American Minister to Norway, return in the same vessel. The transport would "likewise bring back to this country such Americans in Scandinavian countries as can be accommodated and as may not be able to return safely in any other way."
American Legion--her neutrality shown clearly by the U.S. flags painted prominently on her sides--sailed for Finland on 25 July, and reached Petsamo on 6 August, as scheduled. On the 15th, se embarked Crown Princess Martha of Norway, and her three children, the Princesses Regnild and Astrid, and Prince Harald. The Army troopship also embarked a host of American nationals and refugees from a variety of countries: Finland, Estonia, Latvia, Lithuania, Sweden, Norway, Denmark, Germany, and the Netherlands, the total number of people being 897. Among the passengers was a young Danish comedian and musician, Victor Borge. The American Legation in Stockholm, Sweden, also consented to the embarkation of 15 "prominent nationals of American republics . . . including the Mexican minister . . . ."
Unbeknownst to probably all but a handful of individuals, American Legion also took on board an important cargo during her brief stay at Petsamo. Before she sailed on the 16th, after an almost Herculean effort involving taking this special cargo by truck the entire length of Sweden, the transport loaded a twin-mount 40-millimeter Bofors antiaircraft gun, "equipped with standard sight, and accompanied by spare parts and 3,000 rounds of ammunition." The State Department had obtained the cooperation of no less than three governments to make possible the shipment of the Bofors gun: British, Swedish, and Finnish. The move had been made none too soon, for American Legion was the last neutral ship permitted to leave Petsamo.
American Legion sailed for the United States on 16 August, and reached New York, 12 days later, escorted the final leg of the voyage by several American destroyers. The transport unloaded the Bofors brought from Petsamo, whence it was shipped to Dahlgren, Va., where it would be tested, and ultimately adopted by the Navy and produced domestically. Its installation in American warships from late 1942 proved a significant upgrading the antiaircraft capability of the ships of the U.S. Navy.
...
From the listing for the USS American Legion (AP-35/APA-17)
So this would apparently be the last opportunity for someone to leave via sea at the early date of August 16, 1940.
Thought y'all might find the info on the Bofors of some interest as well.
* DANFS: Dictionary of American Naval Fighting Ships
.
by Esa K on 08 Nov 2006 12:46 
Long ago since this post was started, and havent yet thanked Tero T for the effort to find some info on this, may be a bit late but: Thanks Tero for taking time on this. And...