Strauss alone is not enough but a step in the right direction. If we combine this with more tensions during the Cold War in Europe, and some problems to finance nuclear rearmament in other countries of the NATO, we could maybe see under the right circumstances some change, if there is at the time a trend for more and more middle powers to start nuclear weapon programs. Such a hypotetical nuclear weapon program would be limited, and under strong supervision by the NATO allies.
I doubt that (West) Germany even could start a nuclear program against the will or in secret from the other NATO countries during the Cold War, because of the many foreign troops on German territory.
Such a scenario is highly unlikely but not as much unlikely as a 1990ies Germany which tries to develop nuclear weapons without any reasons.
Sorry if I seem rude. Please be sure that my criticism is not about you. My criticism is about the hypothesis you stated.
Such an hypothesis is not only highly unlikely. It mostly is illogical.
The established nuclear powers do not want new members in the nuclear club. The US hegemon does not want its non nuclear allies to become nuclear powers. It wants its allies to spend more in conventional defense, not into nuclear defense.
Everybody understood in 1989/1990 that Germany's reunification would make Germany the number one european power that it had been from 1871 to 1945. This is why Thatcher and Mitterrand tried for a while to oppose Germany's reunification, to delay it, and demanded conditions and guarantees. Not to mention the Gorbatchev whose country suffered the death of 23/25 million people in WW2.
Everybody also understood that although peaceful, Germany however could quickly become a threat again. Quite a lot of pressure had to be exerted on the Kohl government for Germany to acknowledge the Oder-Neisse border.
And everybody understood that if reunited Germany ever became a military nuclear power, the US would lose its position as the hegemon of Europe and Germany would take its place as the hegemon of Europe, reaching the strategic goal of the second Reich and of the third Reich in the two world wars.
You just can't have 4 governments (US, USSR/Russia, UK and France) to be that stupid and that suicidal to turn Germany into Europe's nuclear hegemon. You can have 1. But you can't have the 4. And if one of the four ever supported such a perspective, the three others would band together and cause a crisis in order to block the perspective of Germany becoming a nuclear power.