Our exports are dwarfed by our imports. So it doesn't really matter if exports get hurt some.
At the start of the Great Depression, exports were equal to 4% of GNP. Volume dropped by less half. However because world wide prices had crashed for all products, the dollar value of the decrease was greater. Also note that throughout the roaring 20's, a period of great economic progress, our tariffs were about 22%. The Smoot Hawley tariff was on top of that.
During the Jeffersonian trade embargo, in which almost all international trade was stopped. The price of goods normally imported rose by 30%. But the price of goods normally exported fell by 30%. So there were offsetting price effects in the economy.
Right, so export powerhouse that we were, when the dollar value (note, not %of GDP) fell by two thirds, it was insignificant.