ggdbole, its not your responsibility to pay any taxes for the buyer.
However, you are responsible for collecting the sales tax for all sales made within the state of New York and remitting that tax to the state.
Its up to the customer where ever they are located to pay their own sales taxes on the goods they import.
And its not just the EU countries that have taxes imposed on imported goods, its just that their thresholds are much lower than most other countries. USA also has import taxes if you are bringing in goods from abroad as well and you as the customer would be responsible for paying those fees.