YUZHNO-SAKHALINSK, Russia—United Nations sanctions are forcing Yuri Dyakov to disband his team of 200 North Korean construction workers in Russia’s Far East. His planned solution: fly dozens of the laborers to an unrecognized statelet backed by Moscow 7,000 miles away.

Mr. Dyakov is part of a small but committed group of Russian business owners and ethnic Koreans braving U.S. ire to maintain business ties with Pyongyang. They are waiting as long as possible to comply with sanctions deadlines and lobbying Russian officials...