It depends on the way you read it. Nuclear bombs cause bloodshed. The blood might be vaporized, cooked, or irradiated - but still shed.
I don't think that's what OP meant; rather I read it literally, to mean one day there might actually be a world without war, or at least, a world without violent wars.
>Nuclear bombs cause bloodshed.
No they prevent and drastically reduce bloodshed.
We aren't in a position to answer this one one way or the other.
If things go very wrong they have the potential to take us out. But a non-nuclear WWIII could, also--not by direct kills but by taking down the interconnected stuff that makes society work.
Also, while they serve to prevent direct wars between major powers they cause proxy wars between the major powers.
Tell that to the families of everyone who's died in the Russian war on Ukraine.
You know that Ukraine had nuclear weapons, and gave them up for the promise of never being attacked?
Would Russia have spent the last 11 years attacking Ukraine if it were still a nuclear power?
(Maybe. Dictators are not reknowned for their sanity and good decision-making skills.)
It wouldn't change anything, Ukraine doesn't have the infrastructure to maintain those bombs.