PhD in energy policy - my dissertation focused on (among other things) the history of how power grids evolved.
Nuclear power is not unique or noteworthy as electrical generation schemes go. It's a basic thermal-to-electrical conversion - the exact same technique that coal/gas/oil/biomass/waste-to-energy generation stations use:
- Take hot thing.
- Boil (a whole crapton of) water.
- Force pressurized steam through a turbine to create rotating mechanical power.
- Spin a magnet inside some coils of wire (really honkin' fast).
Step 4 creates electrical current, aka electrical power.
The civilian nuclear power industry is the beneficiary of these treaties not because it's somehow necessary - but instead because it already exists. In policy (and engineering/economics) circles we talk about the "lock-in" effect, aka path dependency. The principle is that once you've decided on a specific scheme, you create further incentives to continue that scheme because the costs of doing so, compared to the costs of switching to another scheme, are lowered by the existence of infrastructure you've already built.
If you never develop nuclear power in the first place, you'd never notice the absence of it.
So the good news is, you don't need anything special to replace it. Coal, gas, oil, anything that makes heat enough to boil water can be used to make electrical power in exactly the same way. If you're wanting something with (near-)zero marginal carbon, solar, wind, biomass, geothermal, and tidal harness are all viable - and if you went that route you'd want a diverse portfolio and to add grid-scale energy storage as well.
As others have observed there's a million reasons to NOT develop nuclear power/weapons, and once that choice is made, you simply use other candidate technologies - of which there's oodles.
My favorite, btw, For power at the same scale, with the same costly investment, and the same (less, really) real estate footprint? Launch your solar power to orbit, beam down with microwaves. Receiving stations replace nuclear reactors, and otherwise you're in the same societal look/feel.