Amir Peay recently opened a distillery in Lexington, Ky., at the site of the James E. Pepper distillery. About 10 percent of his revenues come from exports, and Peay worries that the European Union’s tariffs will hurt his overseas business.

Amir Peay recently opened a distillery in Lexington, Ky., at the site of the James E. Pepper distillery. About 10 percent of his revenues come from exports, and Peay worries that the European Union’s tariffs will hurt his overseas business