The Great Depression resulted from a collapse in domestic demand, not demand for US exports. The tariff was passed after the 1929 stock market crash. Exports comprised only 5% of GDP in 1929. World trade declined 66% from 1929 to 1934. Even if you attribute 100% of the decline in trade to Smooth Hawley (an unlikely assumption), the tariff had at most a negative impact of 3.4% to US GDP.
From 1929 to 1933 US GDP declined by 39%. It is difficult to attribute that decline to a tariff affecting at most 5% of GDP. Industrial production fell by 45% from 1929 to 1932. Most of the decline in US exports was farm products, not manufactured goods.
Even under Smoot, 66% of all imports were duty free and the effective tariff rate was 19.8%. From 1821 to 1900 the effective tariff rate on imports into the US averaged 29% with only 8% of imports being duty free.
Federal Reserve action shrinking the money supply by 30% contributed much more to the Great Depression than a tariff impacting at most 3.4% of GDP.