So I don't have demographic data on this available. But the reason I don't have it is partially because I think you have some erroneous impressions of how Jewish denominations work. So I'll explain that, and then go backwards and answer what I think your question is.

It's fairly common today for people to think that a Hasidic (also spelled Chasidic) Jew is the sort of Jew wearing the stereotypical Orthodox garb--black suit, white shirt, peyes (sidecurls), beard, black hat, etc. But, this is not the case. Chasidism (from Hebrew hasid, meaning "pious") is a particular theological movement that developed in early modern Eastern Europe. It was bitterly opposed by misnagdim (meaning "opposers"), who objected to various theologies and practices the Chasidim championed.

Now, Chasidism only existed as a movement in Eastern Europe. In Western Europe, and all the more so outside Europe, Chasidism wasn't a "thing". It'd be like asking whether or not ancient Romans were anti-vaccine--they weren't, technically, but because that classification didn't exist at the time, not because they actually had an opinion on that. It's particularly misleading in this case because some of the main beliefs and practices of Chasidism were also big in the Middle East. The Chasidic liturgy, for example, borrows quite heavily from that of the Middle East. So, they weren't all misnagedim either.

Now, what I assume you're referring to as "Hasidim" are modern black-hat groups--the sort of Jews that wear distinctive garb. Not all of these are Chasidim--they're a subset of them. And Chasidim themselves are a rather diverse group, though the differences between them are not immediately apparent to outsiders.

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So, to your original question--to what extent were Jews living a traditional religious lifestyle prior to WW2? This is still not easily answerable. There is a spectrum for this sort of thing. However, in Western Europe, Jews were generally fairly secular--they no longer spoke a distinct Jewish language, by WW2. But that doesn't mean none were religious--many were. But the dominant form of Judaism was Reform, which rejected traditional Jewish observance. In Eastern Europe, fewer secular, but comparison is hard. There was no non-traditional religious movement the way there was in Western Europe. The only decent metric I can come up with are the Jewish political parties in prewar Eastern Europe. Here, too, it's a bit difficult, because in national Polish elections Jewish parties ran as one Jewish bloc, but were separate in local elections. But in Latvia, while the largest two Jewish parties were religious parties, almost 1/3 of votes for Jewish parties were for secularist parties. But Latvia is a small sample, and it's certainly not the case that all secular Jews voted for secular Jewish parties, and that all religious Jews voted for religious Jewish parties.

So, hopefully that gives you a picture. Western Europe was mostly secular. Eastern European Jews were generally more religious, but there's no exact dichotomy for this, and fitting it into a black-hat style metric is problematic. I've ignored the Middle East entirely, because this sort of religious/secular spectrum is even more difficult to make outside Europe.