While nuke launching capacity might stay intact, the discovery / tracking might not. So let's say NK launches 10 nukes that land in Russia and 10 nukes that land in the US.
I’m not an expert on these kinds of devices so take this with a grain of salt, but it’s my understanding that while radar cannot be shielded, sonar can.
Satellite based launch detection would likely suffer. Literally one detection method we use is measuring ionospheric disturbances caused by a rocket punching through the atmosphere. I’d imagine a solar storm is going to A) Destroy the satellites that measure this and B) generate enough ionospheric noise to invalidate the monitoring.