He conducted both internal operatic repertoire and stage works by Ukrainian composers, and took the opera company on tours throughout Europe, Canada, and Japan.

According to a 2011 interview, Kozhukhar was drawn to conducting at the age of 18, when he was enrolled at the Kyiv Conservatory as an instrumentalist who also composed music as a hobby.

He also spent much time studying orchestral scores, which caught the attention of fellow students and, later, school administrative staff.

[3] Kozhukhar also continued post-graduate studies in conducting with Gennady Rozhdestvensky at the Moscow Conservatory.

[3][2] In 1989, he became chief conductor of the National Opera of Ukraine in Kyiv, where he led classical repertoire, and also works by Ukrainian composers including Lysenko's Taras Bulba, Lyatoshynsky's The Golden Hoop, and Yevhen Stankovych's 2001 ballet Vikings.

[5] In 2019, Kozhukhar programed the work with Rimsky-Korsakov's Scheherazade,[5] wherein the choreography by Michel Fokine was revived.

Performances that he led on tours included Tchaikovsky's Mazeppa in Paris in 1992, Verdi's Nabucco at the Strasbourg Music Festival of 1993, and Shostakovich's Katerina Izmailova in Naples.

Later he was also known as "The Computer", a nickname which Kozhukhar said he enjoyed: Keeping in mind that a conductor has got to think faster than everyone else sitting before him, I am not offended [by the name].

[4] Kozhukhar recorded works by Ukrainian composers such as Borys Lyatoshynsky, Andriy Shtoharenko, Lev Kolodub, Vitaliy Hubarenko, and Myroslav Skoryk.