Orion was probably doable with 1970s tech.
It wasn't the bombs, as much as the pusher plate
But an Orion style craft's biggest advantage is getting gigantic spacecraft off the ground. You NEED to have tonnes of mass to absorb the impulse of atomic bombs going off regularly. The other thing is an earth launch Orion would be an Apollo frequency thing - you'd likely only launch one a year or so.
If you tried using one as an Earth orbit tug, on a regular basis, you'd be be fouling up cis-lunar space something fierce with energetic particles, EMP, etc. What they'd do to the Van Allen Belts, I don't want to know. Or unshielded electronics on earth.
Again, with Orion, if it's only once a year or so, you can have everyone in the Western Hemisphere shut down all electronics on launch day. If you need to.
A regular tug? Not so much.
......
AFAIK, the best space nuclear reactor so far has been the TOPAZ reactor the Soviets built. That was ground tested in 1971, and was rated for 5kWe for 3-5 years, although the only two flown apparently only operated for 6 months and a year.
That reactor apparently uses 12kg of U235 fuel, with a total reactor mass of 320kg.
This reactor, and the BES 5 reactor (2kWe, much heavier) used in the Soviet RORSAT (radar sat) program, e.g. Kosmos 954 that crashed in Canada, used thermionic conversion to turn heat into electricity. This has the advantage of no moving parts - but is relatively low efficiency.
Thermionic converters (not nuclear) only had their first prototype in 1957, and one clearly needs time to develop them, increasing efficiency, finding what might work with your reactor, etc.
So. A reactor powered ion engined mission to the Outer Planets is probably only possible iOTL in the mid 70s by the Soviets, and that if they wanted to throw a bucket of money at it.
How early could you push that forward? With a PoD of, say the end of WWII?
Hmmm... With luck you could get the thermionic converter a few years earlier. Ion engines and building the nuclear powered satellite would take a bit. ... Plus you need satellite reliability to be good enough for a multi-year voyage.
Late '60s?