Having a whole space program without Atomic Energy is not a problem as the two things are largely unrelated.

Managing a whole set of space flights without numerical computers is much harder to imagine.

In order to do so you would need to have some kind of mechanical computers much better than what available (partly due to obsolescence of what available (e.g.: Olivetti Dvisumma 24) due to rise of electronic calculators).

The real problem, though, would be how to prevent quanta discovery. It would not be enough to have Max Plank to have an accident before his discoveries. History of Science have multiple examples that discoveries are almost never really linked to a physical person, but at a general "ripeness" of cultural society of the time.

There are several examples of multiple, independent, discoveries of essentially the same thing at almost the same time. Everybody knows what Lobacewsky did to Geometry, but almost none remembers Bolyaj.

OTOH if someone was really "ahead of the times" often died without honor, possibly to be remembered many years (sometimes centuries) later; this is what happened to Evariste de Galois and Gerog Mendel, among many others.

In order to steer our history away of transistors "killing Plank" won't suffice; you need to come up with a complete steering of the whole technology (toward mechanical devices, for example), but it's difficult to imagine a Space Race without a corresponding race to miniaturization... which will inevitably lead to the "infinitely small" and its quantization.

Having a whole space program without Atomic Energy is not a problem as the two things are largely unrelated.

Managing a whole set of space flights without numerical computers is much harder to imagine.

In order to do so you would need to have some kind of mechanical computers much better than what available (partly due to obsolescence of what available (e.g.: Olivetti Dvisumma 24) due to rise of electronic calculators).

The real problem, though, would be how to prevent quanta discovery. It would not be enough to have Max Plank to have an accident before his discoveries. History of Science have multiple examples that discoveries are almost never really linked to a physical person, but at a general "ripeness" of cultural society of the time.

There are several examples of multiple, independent, discoveries of essentially the same thing at almost the same time. Everybody knows what Lobacewsky did to Geometry, but almost none remembers Bolyai.

OTOH if someone was really "ahead of the times" often died without honor, possibly to be remembered many years (sometimes centuries) later; this is what happened to Evariste Galois and Gregor Mendel, among many others.

In order to steer our history away of transistors "killing Plank" won't suffice; you need to come up with a complete steering of the whole technology (toward mechanical devices, for example), but it's difficult to imagine a Space Race without a corresponding race to miniaturization... which will inevitably lead to the "infinitely small" and its quantization.