Unless you believe that they were mainly afraid of Sweden, and didn't give a rat's patoot about the US... (chuckle)
Oh, I don't know -- they might have been a bit concerned about stuff arriving from such far-flung British locations as Canada (chuckle), South Africa (chuckle), Rhodesia (chuckle); not to mention South America (chuckle), and various other ports of call from where British and other non-American merchant shipping were wont to visit. The British merchant fleet was very large, after all, and they went everywhere.
Of course, the issue for American shipping, as far as Germany was concerned, is that they were part of the neutral shipping that was helping to supply its enemy, Britain. In a sense, their dedication to free trade with Britain made all Britain-bound "neutral" shipping a military enemy of Germany.
Any blockade of Britain would have to prevent such shipping from reaching British ports, obviously. And since Britain had control of the surface, Germany's only choice was to use submarines.
As for Woodrow Wilson, his was a choice between allowing American ships to ply the waves at will, without government protection against German submarine warfare; or to apply government force to prevent shipping from entering the battle area; to protect American shipping and become a de facto combatant; or to dispense with the pretense of neutrality altogether, and acknowledge that Germany had crossed the line.
You didn't read carefully. Hindenberg's statement specifically mentioned military as well as economic use of neutral countries. If you don't think that included the direct risk of the US entering the war on Britain's side, then you've already forgotten about the Zimmerman memo that you yourself posted to this thread.