I explored similar scenario here: https://philarchive.org/rec/TURTFO-14

TL;DR: "around 176 000 direct fatalities and 220 million latent fatalities from cancer. Not good, but not an extinction-level event."

A nuclear attack on nuclear power stations

There are around 440 active reactors in the world and the number is not changing since 1988. But energy demands suggest the possibility of a new nuclear renaissance and that much more nuclear power stations will be built.

The worst possible scenario could be imagined: during a war, nuclear-tipped ballistic and cruise missiles are launched at all known nuclear facilities (reactors and spent fuel storage facilities) in all countries. For example, North Korea has threatened to attack Japanese nuclear power reactors.

It was estimated that a 1 megaton bomb is needed to vaporize a nuclear power station and send whole its radioactive materials into the atmosphere. See an interesting discussion of this question here.

However, the main danger is the spent fuel pools which easily could catch fire if left unattended without water, and surely will be damaged after even the smallest nuclear attack. Almost every nuclear power station has such a pool. As an author on Quora said: “To put the extremity of the possible release in perspective at Fukushima, the spent fuel in pool #4 had the potential to release 22 times the amount of radiation into the environment as compared to Chornobyl (#4 pool 568 megacuries vs Chornobyl 25 megacuries). The Fukushima spent fuel pools in total had the potential to release 66 times the radioactivity of Chornobyl and there are hundreds of such sites around the world.” If a pool in Fukushima catch fire, Tokio would have to be evacuated.

The biggest part of accumulated radioactivity is in the spent fuel storages. 240,000 tons of it exist in the world. The total radioactivity of it is 28 billion Tbk (2.8x1022 atom disintegration events per second), according to “Estimation of Global Inventories of Radioactive Waste and Other Radioactive Materials”. The total radioactivity of global spent fuel is 40 000 times more than that of all military sources. Chornobyl accident produced 2 x 1018 becquerels, or 10 000 times less than the total radioactivity of the spent fuel in the world. 

An interesting article tries to estimate the consequences of the worst-case reactor incidents: "Importance of severe accidents radiological releases and definition of large damage." It shows that the complete destruction of a large reactor will cause only 45 direct fatalities but around 50 000 latent fatalities due to cancer. The total destruction of a reactor will release 30 times more nucleotides than Chornobyl did. If we want to get total global fatalities in case all nuclear power reactors will be destroyed, we need to multiply these fatalities estimates by 440 (number of the reactors) and then by 10 – this comes from spent fuel pools. This will give around 176 000 direct fatalities and 220 million latent fatalities from cancer. Not good, but not an extinction-level event.

If this spent fuel will be disseminated all over the world, it will give 5x107 Becquerel’s per sq. m. (EPA norm is 7400 Bk per sq. m. or 1000 times less.) It is not easy to directly convert this into exposition dose in rads. One claim is that topsoil always has 1 curie (=3.7x1010 Bk) per sq. mile of natural radium on the depth to 1 foot, according to this document, which is around 104 per sq. meter, or 1000 times less than what would be produced by a global attack on spent fuel depots. If man natural radioactivity is around 15 mcR-hour and comes mostly from radium, now it will be 15 000 mcR-hour (or 120 R in a year), but it is the upper estimate, as there are other natural sources.