"Where" US Duties were collected is quite irrelevant to the point. Where duties are collected says nothing as to who ultimately pays for them.
Lincoln was also not as concerned about "Where" such duties would be collected as he was that they be collected. Again, PeaRidge posted material that seems to indicate the Union was in a serious deficit condition at the start of the war.
What the graphics I posted demonstrate is that the loss of, say Charleston or Savannah would have little to no effect on Federal Government import duty revenues.
And the Federal Government's financial condition was only critical in early 1861, because of the demands of a rapidly looming civil war.
It took major changes by Congress to hugely increase Federal finances so they could pay for war.
So, if anything, the government's financial situation would have lead Lincoln to minimize expenditures and seek accommodation with the Confederacy.
But that's not what happened.