That was 30 years ago. If I remember correctly, none of the sites that designed and/or assembled warheads were in what now is Ukraine. They wouldn’t have to start from scratch, but even having the old blueprints will only go so far and any institutional knowledge from people involved in the Soviet Union’s weapons programmes will have more or less died with them. Simply rebuilding an old design would require matching parts. Which probably aren’t available in Ukraine anyway and would have to be sort of reverse engineered and rebuilt using whatever is available now. Machined parts are one thing, but the electronics could be tricky. And so on.
The fissionable material would have to come from spent fuel rods which of course is possible. But apart from extracting plutonium and enriched uranium from nuclear waste it would need some serious processing to make truly weapons grade material. The short version is that reactors designed for energy production are not run like reactors designed for making the bomb stuff. This starts with what goes into the fuel rods. Of course all the USSR’s reactor designed started out as piles to make material for weapons and were developed into energy plants from this, so there is bound to be some overlap. I think it also would be possible to modify the reactors currently in use to shift from primarily producing heat towards creating suitable isotopes, but I doubt this would be very efficient with fuel rods intended for energy production. Not to mention that Ukraine is struggling with keeping the lights on as it is.
Entirely possible, but the sheer logistics and resources involved are a real challenge. This would take years, even with a bit of outside help.
Just look at how long it took/takes newcomers to join the nuclear club, especially those with limited resources. Britain, France, China, Israel, India, Pakistan, South Africa, North Korea made it, but it took a while. Iran is still at it. Others dabbled, but dropped out.
The topic pops up every once in a while in Japan and South Korea as well. Public opinion is still firmly against it, but a conflict in Taiwan could change that.