People recognized the theoretical advantages of nuclear energy even in the 1930s (i.e., that you could get much more energy per unit input of fissile material than of coal), so much like solar energy there would probably still be a trickle of interest and investment over time. Rather more pertinently, however, navies (as pointed out by
@riggerrob and
@sloreck) immediately recognized that nuclear energy offered major operational advantages over oil, just like oil had over coal and coal over wind, and would probably have invested relatively heavily in developing nuclear energy for that reason.
Also, you're underestimating how much military tension was present in Europe and elsewhere in the world prior to World War II and the Cold War. There was more than enough incentive for the Germans, Japanese, Americans, Soviets to invest in nuclear technology for their militaries.
Building commercial reactors
is hard, but I'm not sure I would actually say that building a bomb was easier; as pointed out already, the Manhattan Project built a number of reactors prior to building any bombs, and the German program came damn close to putting together something that could reach criticality (see
this article from this month's
Physics Today for a nice analysis). It's not too hard to see an alternate history where the discovery of fission leads to a gradual development of reactors and their refinement by both academic and military programs, with bombs, though recognized as a possibility, continually deferred as being both very expensive and of questionable utility, and the whole thing ending up with reactors developed first.