Reagan legitimately weaponized space with Star Wars, but, it was taken to a new height in later years.

...Characteristically, (click here) on the plane ride home from Europe in July when Bush sent a note to Gorbachev inviting the Malta meeting, the President spent more time (and far more space in his memoir (Note 5) reaching out to the Communist dictators in China who had murdered their pro-democracy demonstrators in 1989, than to the Communist reformer in Moscow who had refused to do so....

At no point in time did Reagan see space as an extension of the nuclear potential of the USA, so much as an extension of Non-Proliferation.

11/2/1989 (click here)
Bush reaffirms US Space Policy, prioritizing US security.

There was still testing that continued.

6/1/1990

Bush and Gorbachev (USSR) sign new protocols to the 1974 Threshold Test Ban Treaty (ratifying it on 9/25/1990) and Peaceful Nuclear Explosions Treaty (PNET) provide for advance notification and onsite inspection of tests above 35 kilotons.

7/31/1991
Using pens made from melted down SS-20 and Pershing II missiles, Bush and Gorbachev (USSR) sign START II, cutting U.S. long-range nuclear warheads by 15% and the Soviet’s by 25%. 

1/28/1992
Bush announces in his State of the Union Address t he cancellation of the Midgetman Missile Program; no additional production of W-88 warheads or MX2 test missiles; t ermination of the B-2 bomber program; and termination of production of the advanced cruise missile.

1/29/1992
Bush postpones production of nuclear warheads for Trident II and W-88.

Peace was an agenda with President George H. W. Bush. He intervened with the Lisbon Protocol as well. But, this time it would be with the First Russia President Yeltsin.

The United States and Russia (click here) reached a solution to this complex problem by engaging Belarus, Kazakhstan, and Ukraine in a series of talks that led to the Lisbon Protocol. That agreement made all five states party to the 1991 Strategic Arms Reduction Treaty (START), which required Washington and Moscow to each cut their deployed strategic nuclear forces from approximately 10,000 warheads apiece to down below 6,000 warheads on no more than 1,600 ICBMs, submarine-launched ballistic missiles (SLBM), and long-range bombers. The protocol signaled the intentions of Belarus, Kazakhstan, and Ukraine to forswear nuclear arms and accede to the nuclear Nonproliferation Treaty (NPT) as non-nuclear-weapon states, a commitment that all three fulfilled and continue to abide by today.

Estimated Warheads in Belarus, Kazakhstan, and Ukraine in 1991

Strategic Warheads	Tactical Warheads
Belarus	100	725
Kazakhstan	1,410	Uncertain
Ukraine	1,900	2,275

6/17/1992
Bush and Yeltsin ( Russia ) agree on the Joint Understanding, which forms the basis for the Strategic Arms Reduction Treaty II (START II).