It seems to me that the British were able to pressure Dutch companies into not trading with the Germans (and despite this the Dutch, like any neutral country in any world war, still re-exported products to the Germans, as neutral countries seem to use wars to earn as much money as they can)
Luxury items...not such a big deal in Hearts of Iron, especially once Germany is at war with the UK. Anything produced and manufactured in Netherlands probably you can make fair game to Germany. The things the Netherlands had that Germany actually wanted were raw materials, oil and Rubber from the Dutch East Indies which is what the
Nederlandsche Overzee Trustmaatschappij was intended to regulate.
I think there is a difference between Iceland and the east indies, Iceland didn't have any major amount of important raw resources and the Dutch thought at the time they needed their colony for economic reasons, apart from that, the Netherlands were extremely neutral until the Germans violated their neutrality, up to shooting down planes of both sides, so I think they would not like it if the British suddenly invaded their rich colony. I am almost certain that would've lead to the Netherlands joining the axis, or at the very least aligning to Germany and aiding them. Even if that were only because the public opinion in the Netherlands would become anti-british...
I don't think it would come to that, unless the Netherlands player really wanted to boost Germany against their own interest.
Germany: "Extremely Neutral Netherlands, sell us your stuff."
Netherlands: "OK, we have an assortment of Tulips and Heineken, take your pick."
Germany: "We don't want that stuff. We need oil and rubber."
Netherlands: "What can you give us for those resources?"
Germany: "We can spare a bit of coal. Some older weapons. And Reich-marks, we'll pay you back after the war because we're totally going to win."
Netherlands: "Wow, that deal sounds...awesome. Why don't you buy oil from the Russians?"
Germany: "They want our steel and machine tools. We give them as little as possible because they are scary. We'd rather trade with you."
Netherlands: "Sadly our oil and rubber is overseas

. You conquered our only other neighbor so the British Navy is not letting us import any for re-export. Get rid of that British Navy, then we'll deal."
*Germany fights Battle of Jutland 2.0*
Germany: "Smuggle stuff in and sell it to us."
Netherlands: "The British have a bunch of spies here, this is the spy capital of the world now. They'll find out and not let us import anything."
Germany: "UK is a bully. Join us and fight with us."
Netherlands: "I agree UK is a bully, but not even the United States wants to go to war in order to sell you stuff on credit. Besides, the UK is actively co-administering our colonies while this war is going on. We'll lose our colonies faster than you can say 'Italian Somaliland'"
Germany: "Gah! Give us oil or we will attack you!"
Netherlands: "Now who is a bully? You could attack us, and you'll win, but then you'll lose access to our domestic markets and you still won't get any raw resources."
Actually if the Netherlands insisted on trading raw resources with Germany, the Allies (UK + France) wouldn't have to seize Dutch shipping (though they probably would anyways). The allies could simply refuse to let the Dutch use their refueling stations and Dutch merchant ships wouldn't be able to reach the East-Indies.