South Korea and Japan are countries which have breakout nuclear weapons capability. Both of them had laser uranium enrichment programs at one point. Both have extensive civilian nuclear industries. And they have the solid rocket technology to make the delivery systems.
Solid rocket is just part of the question. Those are necessary, not sufficient, conditions. The big question is miniaturization which is a totally different game. There's tons of secret and non commercial components and capabilities like x-ray mirrors, inert atmosphere machining, etc.
In terms of real enrichment capability, laser is too low volume. You need centrifuge or diffusion.
Russia is #1, EU is #2, China #3, US #4 with enrichment capability in 4000+ (US) to 27000+ (Russia) separation work units.
Entire rest of the world (including Japan, SK, India, Pakistan, etc) combined is 66 SWU.
SWU is also transferable between low enrichment high volume and high enrichment low volume, so it measures both enrichment level and total capacity.