US Nukes: 7300
Russia Nukes: 8000
India Nukes: 90-100
Pakistan nukes: 100-120
Everyone except the US and Russia nukes: ~1100
(source: https://www.independent.co.uk/news/world/nine-nations-have-n...)
There's a reason they were all proxy wars and they never escalated into direct conflict on the scale of WWII (or beyond), and that reason is nuclear deterrence.
Nukes don't prevent “any war” from happening between powerful nations, though they do seem to have some utility in restricting the escalation of such conflicts.
(Now, you could argue that unilateral conventional disarmament would leave no choice but to escalate to nuclear war, which would improve deterrence and prevent even small scale conventional, politically-covered attacks, but that argument would be highly speculative.)
100 nukes is powerful enough.
So, in the universe you are writing from, the Kargil War would have been an impossibility?