Depends on what you mean by "effectively". Yes, you can absolutely have nuclear weapons without nuclear power infrastructure, North Korea and Israel both have nuclear weapons, but no nuclear power programs.
Having a civilian program makes things a little easier, or at least easier to hide. Italy does have a tiny uranium reserve, which it never mined, but I'd guess that they'd need to buy the uranium they'd need for a nuclear weapon. That's a bit easier to do, if you can disguise it as nuclear fuel.
I don't know how effective are NK nuclear weapons, but Israel would definitely count. But according to WP[1], Israel has "research reactors" which might or might not have military use.
