Unlikely. Using any form of nukes for such a small conflict (inflated by the NATO rona dhona) will only isolate Russia more. It would be extremely hard for us and China to even tacitly support him that we are doing now. Based on the troop movements, Russia is redirecting its forces for PLAN B; capture entire South & East of Ukraine and turn the Galicia region into a land-locked shadow country where Ukrainian neo-Nazis and other Galicians such as Poles, Moldovans, Hungarians, etc., keep fighting between each other and bog NATO's resources.
Making Ukraine landlocked is in Russia's interest, as the entire Black Sea now becomes a dominion of Kremlin (along with Turkey). Contrary to what NATO liberals are claiming, they cannot completely shut off Russia as it would be in control of all the popular wheat-growing areas. While we have managed to plug the gap of export shortfall this year, but we are not a perennial solution. 90% of what we grow in terms of wheat is consumed and strategically stored for use within India, much like China's industrialized farming sector.
Russia will therefore become indispensable for the food security of European countries. They can't simply expect the entire world to divert their supply chains from existing markets to them alone.
Coming back to Sweden and Finland, a more practical move for Putin would be to reach out to Sweden and Finland and give them written guarantees (in secret) that he'd not touch them if they don't join NATO. Threats won't always work especially when so many countries are trying to band together. If he can assure Finns and Swedes secretly, that would take some pressure off Russia.