Continuing...
The main application for the Soviet PNE program was deep seismic sounding. I don't know if that's something the US would find useful or not, but the Soviet project was apparently quite successful. And, since the shots were fired deep underground, there's no risk of fallout escaping to the environment as long as you don't fire them on top of a water table or something equally stupid.
Nuclear stimulation of natural gas could probably work, in a world where radiation is less of a big deal. The Soviets did this more then once, and apparently found it a useful technique. Similar arguments apply to breaking up rock for hydraulic mining. In both of these techniques, the product may be contaminated, but there's no general release of fallout into the environment, so safety is much easier to ensure - if the output is too radioactive, just don't sell it.
There are two key issues here that need to be addressed, though, in all of these potential applications. First, nuclear proliferation. This has three aspects: first, if this is in a world where the Nuclear Non-Proliferation Treaty still happens, the Treaty guarantees the right of states to "peaceful nuclear technology". Which means that, if PNEs are operationalized, the US is - at least theoretically - obligated to every non-nuclear state to provide them with PNE services. Second, it offers a ready-made excuse to non-treaty nuclear states that want a bomb - "it's not a weapon, it's for peaceful purposes!" India actually used that excuse for their first nuclear test IOTL. Third, we're talking about making a lot of devices and shipping them around the country to be used for commercial purposes - the studies on natural gas stimulation were talking about hundreds or thousands of devices per year - so there's a real risk that one of these things is eventually going to be stolen.
Second, radiation. Assuming a reasonably competent but not superhuman US government, it is very unlikely that anyone will be exposed to doses of radiation in excess of 100 mSv, and most will be more in the range of 10 mSv or less. To cause acute symptoms, you need to be exposed to at least 1,000 mSv. The thing is, we don't actually know what doses of radiation below 100 mSv do to you. We don't really know if they're dangerous or not.
We know that the risk of cancer to the individual is low - a 100 mSv dose carries about a 1% increase in lifetime cancer risk, and that above 100 mSv, the risk scales roughly linearly (so 200 mSv = 2%, 300 mSv = 3%, etc.). The Linear No-Threshold hypothesis (LNT) assumes that the effects continue to scale linearly below 100 mSv: 10 mSv = 0.1%, 1 mSv = 0.01%, etc. The Linear Threshold hypothesis (LT) assumes that there's some threshold - usually somewhere between 10 mSv and 100 mSv - below which there's no increase in risk. We genuinely do not know which hypothesis is correct; the data is inconsistent. Right now, the assumption by public regulatory agencies is that the LNT hypothesis is correct, on the grounds of "better safe then sorry". But the AEC in the '50s and '60s assumed that the LT hypothesis was correct - and there are good arguments that they were right.
The reason this matters is that, in something like Plowshare, millions and millions of people are going to be exposed to very, very small doses of radiation. If LNT is correct, and you expose ten million people to 1 mSv of radiation, then 10,000,000 times 0.01% = 1,000 people will get cancer who otherwise wouldn't, and half of them will die of it. If LT is correct, they will be perfectly safe. (And it's worth pointing out that 1 mSv is well within the variation of natural radiation exposure).
Now, in the real world, I think shifting to LNT was the right decision. Better safe then sorry. But, I think it's likely that, if public fear over nuclear energy had not grown so extreme, the LT hypothesis would have remained the dominant position of US regulators. And this means that the safety issues of Plowshare - and other exotic uses of nuclear energy - can be overcome with sound engineering. (This also, by the way, means that nuclear energy becomes a lot cheaper.)
So why did public fear of nuclear energy become so extreme? People in the '50s were probably too blase about radiation, but the modern attitude has gone even further in the other direction. Frankly, I'm not really sure why. The usualy answer is a combination of "radiation plays into psychological fears of contamination" and "fear of nuclear energy is a displacement of fear of nuclear war". I don't find either argument entirely convincing, but I can't really offer a better answer.
So, to sum up this already-too-long post, because I need to go to a meeting: an atompunk timeline with a successful Plowshare is probably possible, though nuclear excavation will probably be confined to a political rather then economic endeavor. But this depends on deeper issues within public consciousness, which may require a pre-Cold War PoD.