short answer is no, the weapons are subject to US jurisiction and under the terms of the SALT treaties
would not be able to be transferred to another country.
From Wiki:
Ukraine had 220 strategic weapon carriers on its territory, including 130 RS-18 (SS- 19), 46 sophisticated RS-22 missiles, and 44 strategic bombers carrying 1,068 long-range cruise missiles. In November 1993, the Ukrainian parliament adopted a resolution On the Ratification of the Treaty Between the USSR and USA On the Reduction and Limitation of Strategic Offensive Weapons of June 7, 1991 and the Protocol to the Treaty of May 23, 1992. The next stage was the signing on January 14, 1994 of the Trilateral Statement by the Presidents of Ukraine, Russia, and the United States under which Ukraine was to destroy all nuclear weapons on its territory, including strategic offensive weapons.
Ukraine, Washington and Moscow reached an agreement in January that allowed for the dismantling of Ukraine's 176 Intercontinental ballistic missile (ICBMs) ahead of Kiev's formal ratification of the Nuclear Non-Proliferation Treaty (NPT). France and China provided unilateral security assurances in the form of diplomatic notes. The missiles—130 SS-19's and 46 SS-24's—carried about 1,800 nuclear warheads altogether.
Before voting on accession, Ukraine demanded from Russia, the USA, France and the United Kingdom a written statement that these powers undertook to extend the security guarantees to Ukraine. Instead security assurances to Ukraine (Ukraine published the documents as guarantees given to Ukraine[3]) where given on 5 December 1994 at a formal ceremony in Budapest (known as the Budapest Memorandum on Security Assurances[4]), may be summarized as follows: Russia, the UK and the USA undertake to respect Ukraine's borders in accordance with the principles of the 1975 CSCE Final Act, to abstain from the use or threat of force against Ukraine, to support Ukraine where an attempt is made to place pressure on it by economic coercion, and to bring any incident of aggression by a nuclear power before the UN Security Council.
Ukraine was scheduled to submit its instruments of accession to the NPT as a non-nuclear state and formally enter into START at the OSCE summit in Budapest in December 1994. The Rada resolution on accession to the NPT, however, was ambiguous as to whether Ukraine was acceding as a nuclear or non-nuclear state, which was unacceptable to the Russians. The compromise reached after intense negotiations was to attach a diplomatic note from the Ukrainian president to the Rada resolution stipulating that Ukraine was acceding as a non-nuclear state.