Okay, so lets say you figure out a way to build a desktop-sized nuclear power plant that doesn't produce any radioactivity. And, to keep it simple, lets say there's no other unusual, unexpected properties to do with safety.

We'll use it, and we'll use it a lot. It'll power the next generation of EVs, for example, and lithium batteries might be relegated to a few rare niche uses only. You wouldn't need to charge it, you'd just replace it every couple decades. If it's cheap it might find it's way into lesser appliances and devices as well. It's possible the biggest impact will come from things that wouldn't even work without that much energy density, and that we don't have a name for yet. If the devices are really cheap it might become a nuisance or environmental hazard, like wonder-material plastic has.

The one big issue it could have, is if there's a way for all that energy to release suddenly. You've explicitly ruled that out, though. (And for what it's worth, it's very, very hard to make real nuclear reactions finish both completely and quickly, to the point it just doesn't happen by accident. It's even hard to make happen on purpose)