If we uncontract 振んなきゃ, we find that it's undergone these three contractions:
振らなければ → 振らなけりゃ (eba → ya)
振らなけりゃ → 振らなきゃ (erya → ya)
振らなきゃ → 振んなきゃ (/ran/ → /rn/ → /Nn/)
In other words, the full form of 振んんなきゃ means "If [you] don't swing [the bat]". That's conditional, though, so something should come after it; and if nothing does come after it, we can infer that the rest of the sentence has been deleted:
...which is why なきゃ on its own can have that meaning. However, in this case you cannot infer that ならない has been deleted, because it follows as part of the rest of the sentence. In this case, the consequence of not swinging is 話になんない. Let's uncontract that, as well:
話にならない → 話になんない (/ran/ → /rn/ → /Nn/)
In this case, 話 means "a topic of discussion" / "something to talk about"; see sense 3 at 大辞泉. So the phrase 話にならない means "[won't] become something to talk about". See also the entry for the phrase itself in 大辞林, which says (among other things):
...which I would translate as "to have no value as a topic of discussion".
Put it all together:
As you can see, it doesn't literally mean "nothing can happen". I would translate it somewhat literally as follows:
Anyway, if [you] don't swing the bat, it won't be worth talking about.