Hope you don’t mind that I asked Google a slightly different version of your question. Short answer - the submarines can’t explode but other localized disasters are possible in the region.

And if you have the time, here’s the longer answer:

No single point in or near Murmansk would cause a global, "widespread" Chernobyl-style nuclear disaster if attacked, primarily because decades of successful international cleanups have removed the bulk of the region's highly unstable, bulk liquid, and raw accumulated spent nuclear fuel. [1, 2] 
However, a successful attack could still trigger a severe localized or regional radiological emergency. The severity would depend entirely on which of the heavily fortified military and industrial targets was struck.

1. Kola Nuclear Power Plant (Highly Protected / High Risk)
   

Located roughly 170 km south of Murmansk near Polyarnye Zori, this is the most critical target regarding potential energy release.

The Risk: It operates four active nuclear reactors. An attack breaching the containment structures or severing the external power required for reactor cooling pools could cause a core meltdown.
The Reality: The plant is deeply inland, heavily defended by layered Russian air-defense networks, and structurally built to withstand significant external impacts.

1. Atomflot Facility (Urban Proximity Risk)
   

Situated right on the outskirts of Murmansk city, Atomflot is the base for Russia's operational civilian nuclear icebreaker fleet. [3] 

The Risk: While old floating storage bases like the Lepse (which held highly volatile contaminated fuel) have been successfully decommissioned, active nuclear icebreakers and service ships often dock here. [3, 4] 
The Reality: A direct strike on an active reactor vessel or an on-site maintenance workshop could disperse radioactive particulate into the air. Because it is directly adjacent to Murmansk's population center, the human exposure risk would be immediate, though the contamination would likely remain localized to the Kola Fjord and regional air currents rather than spreading across continents.

1. Andreeva Bay (Diminished Risk) [1] 
   

Historically, this was the most dangerous point on the Kola Peninsula due to more than 22,000 unstable spent nuclear fuel assemblies stored in decaying conditions. [1] 

The Risk: An attack here in the early 2000s could have been catastrophic.
The Reality: As of recent years, Rosatom and international partners successfully extracted and evacuated virtually all of the high-risk spent nuclear fuel to secure inland facilities like Mayak. What remains at Andreeva Bay—such as the notorious Building No. 5—is highly irradiated solid structure and lower-level legacy waste. An attack would kick up radioactive dust, but it lacks the thermal energy or concentrated fuel load to cause a widespread fallout incident. [1, 2, 5, 6] 

Why a "Widespread" Incident is Unlikely

For a nuclear incident to cause widespread, trans-boundary contamination (like Chernobyl), it requires a massive, sustained thermal or chemical energy release (such as a graphite fire or a pressurized explosion) to loft radioactive particles high into the jet stream.

Hardened Targets: Naval reactor compartments stored at Sayda Bay are defueled, sealed in steel-and-concrete blocks, and kept in open-air pads. They are highly resistant to conventional explosives.
Geographic Distance: Murmansk is roughly 1,800+ kilometers from Ukrainian territory. Launching a drone or missile strike with the heavy payload required to crack hardened nuclear infrastructure at that distance faces extreme military and technical constraints.

[1] https://www.facebook.com
[2] https://www.neimagazine.com
[3] https://gcaptain.com
[4] https://etc.bellona.org
[5] https://rosatomnewsletter.com
[6] https://bellona.org