Given the CEP they were aiming for, and amount of time they had to fiddle with them, I'd guess they started very carefully with the physical precision of components.
The radius of a circle within which 50% of rounds will be found.
For the V-2 rocket this was 4.5 km.
For the Minuteman III missile, 240m.
Blast effects decrease with the cube of the radius, so a more accurate weapon means a smaller effective warhead. The "Flying Ginsu" AGM-114 Hellfire missile has a CEP of 5 meters or less, and uses blades rather than explosives to minimise any unintended casualties.
But then withdrawn from service due to treaty, because with that accuracy, first striking your target's silos and hardened facilities starts to be a viable option.
Sometimes you can be too accurate.
Also, related, the W76-1/Mk4A height-adjusting fuze solved this this in a different way, by recognizing that there's a 3D kill-volume (above and around the target) rather than a 2D kill circle.
Consequently, if you aim beyond the target and have your warhead measure actual height vs expected once on a ballistic trajectory, you can adjust the fuzing height to detonate within the volume, even if you overshot the target. See figures 2 and 3. https://thebulletin.org/2017/03/how-us-nuclear-force-moderni...
Un/fortunately, this puts us back into viable first-strike territory.
Based on pictures the CEP should be very small, centimeters maybe.
This missile doesn't explode, instead it send 6 blades at the target. Pictures show direct hits.
I'm well aware, and that was my take, and I was initially going to write "within a metre", but couldn't find substantiation of that. The Hellfire itself offers the 5m value.
https://navsource.org/archives/08/PolarisHistoryGEX1.htm (see bottom / appendix for examples of Polaris-era INS)
Given the CEP they were aiming for, and amount of time they had to fiddle with them, I'd guess they started very carefully with the physical precision of components.