What if developing nuclear weapons was physically impossible?

Then mustard gas .chemical weapons would eb considered mad in that time line i presume.

Wait a second...

with no nukes both sides have large bomber fleets in their armament.
But you still can´t wipe out a city or large area of the enemy - because you lack that kind of WMD.

To achive this, you need either a much more effective chemical weapon (nerve agents that could survive months or years in a contained area) or biological weapons.

These are quite succsessfull, because you need one person say in New York, that start to infect half of the USA untill the illness starts.
The "perfect" weapon cause death with say 40-50% ratio, but only after some very long, painfull illness. Basically you need a "slomo" Ebola... with say 3 months incubation time... if you do not try to keep your people alive you destroy the stability of the society (in modern democracies), but you can´t fight if 20% of the people of your country dies. 

These weapons don´t need huge and expensive preparations... 

if we drop this nasty book, we stay with the very expensive conventional bombers.

These would go from "B29/32" to B52 and then to very enlarged huge B52 on steroids, able to reach an enemy area with 1000km/h from 10.000km distance and drop 150ts of explosives... 
All in "cheapish" planes, that could be massproduced.

to protect em you need long range jets and Anti-Missle-weapons... all without nukes...

But we will see no nuclear submarines that carries 12-24 Missles with 1-10 nukes for 10-15 billion dollar each ship/weapon system...
so if you could build a modernised "better" B52 for say 10 Mio USD each, you could finance 1000 of these babies for one Boomer. 

The big problem with them - sometimes in the 60ties they are obsolete, because AA-weapons are to good.
To move 10k tons of explosives with huge missles is way to expensive.


The two superpowers will propably inform each other about some biological "superweapons", these could combine Influenca with Ebola, Yellow fiber, AIDS and cholera But smaller countries face a huge problem.
Think about Israel. Nobody announce it, but everyone accept the fact that Israel has around 100-150 nuclear devices. So nobody really try to kill the israelis (wipe em out). The backslash of such move would be killing your country (OTL). Here - this is missing.
So Israel needs to defeat much larger enemy countries - this could only work with either deadly chemical weapons (think about some "VX-gas Cairo-scenario") or biological weapons. 
Esp. the chemical weapons could be much earlier used instead of nukes. Nukes from Israel is the "last defence" - if some arabian enemy seem to "terminate the jewish people" as they promised "at home". If you face some ugly and problematic defeats - say 1973 the first days - you could - as long as you have an airforce - let the arabs in egypt suffer NOW. The same is true for the enemies of israel. Think about syria in 67, they could shell Jerusalem with chemical weapons... nobody would try this in OTL, not only because of the israelian nukes but also because of chemical weapons are banned. (better "were banned" - some people use em in syria now). In a world without nukes chemical weapons would be used more often, so syrian VX-gas or sarin-derivates would ne no "incredible crime" but common warfare of these days. 

As strange as it sounds - the world would be much bloodier as OTL, because the nukes made clear that if you use WMDs, the others will use their nukes to punish you. 

By the 60s, the US and USSR have developed artificial epidemic viruses perfectly adapted for each country's conditions, making them extremely effective when deployed correctly. This new kind of biological weapon attacks the host's body and spreads, having devastating effects.

For the Americans, it is known as Horseman-5V
For the Soviets, it is known as VXX-9

Each nation works desperately to perfect their own weaponry. By 1967, America has three factories in Alaska, churning out hundreds of thousands of tons of Horseman-5V. The Soviets, lagging behind technologically, only have a single, less powerful factory in northern Siberia. By 1968, the US has 4,000,000 tons of Horseman-5V, enough to reduce Eastern Europe into an inhospitable, disease-ridden wasteland. The USSR, on the other hand, possesses 1.2 million tons of VXX-9, still enough to wipe out 99% of every human on the East Coast and southeastern Canada. They will spend the following years perfecting their technology, making it evolve so it can overcome natural human immunity many are randomly born with. If lucky, no nation will ever have to use their devastating weapon of hell.

Its actually not to hard to genetically modify a virus at one's choice. They can make it as brutal and slow as they wish to be. They can modify the bubonic plague so it is immune to modern medicine, airborne and extra painful and gruesome. That's can also work as a propaganda machine: "Look what we can do! We're better and more powerful!" Really interesting nevertheless. 

Yeah. Pretty much. If a biologic war does break out, it is likely many - as much as a few hundred thousand - may survive due to natural immunity. Also, keep in mind each country can easily prepare for such things. Spies can deliver specifications for the enemy virus, so a cure can be developed. It is easier to overcome a virus attack than an obliterating nuclear hell.