You underestimate how easily a primitive Scud type rocket can be mated with a dirty nuclear warhead. Even if low on yield and accuracy it an sure wreak havoc on densely populated areas of Europe and Israel.
No, since I used to be a targeting and launch officer for nuclear missiles.
As a launch platoon officer I regularly mated and unmated the HE and nuke versions (training) to the Lance missile.
However, it still isn’t a nuclear missile unless you put a nuke warhead on the thing.