While I've never come across the statistics regarding this particular question, I just wanted to note that in the Nazi context, being a Jew wasn't based on religion at all. While earlier forms of European antisemitism did focus primarily on the religious aspects, by the time the Nazi Party came to power, being a Jew came down to physical features/ blood relations which defined individuals as Jews. In fact Daniel Goldhagen argues that long before the Nazi's came to power, Germany was already engaged in "eliminationist antisemitism" which viewed Jewish blood, people, and culture as inherently incompatible with German culture and values. While the Holocaust involved outright killing people of and thought to be of Jewish descent, early attempts at eliminating Jews from German society took place in the form of granting them more freedoms in the hopes that they assimilated into German society to the point where "Jewish" values would disappear.

I actually gave a presentation on an oral history done with a Polish Jew named Walter Grosfeld earlier this week and within the interview he stated that his family wasn't very religious at all. They celebrated the major holidays, but said other than that his family wasn't devout.

So I guess in the context of the Holocaust, how devout Jewish people were in terms of religion didn't really matter. If your physical features or your lineage could define you as a full-Jew or Mischlinge (half-Jew), you were most likely subject to the increasingly harsh racial laws. Jewishness existed within your blood, and the Jewish religion was only a small component of the larger Jewish problem. The Nazi's simply didn't care how devout or non-devout someone was because to them all Jews needed to be eliminated either way.

Sources: Goldhangen, Daniel. Hitler's Willing Executioners: Ordinary Germans and the Holocaust (New York: Random House, 1996)

Link to the California State University, Fullerton's Center For Oral and Public History's "European Experiences in World War II" project. Walter Grosfeld's interview is labeled as OH 4097.

I'm not sure whether such records are available, yet you can make a basic judgment call about it by looking at the locations where the Jews came from. I'll walk you a bit through a potential way of thinking about it, though I don't have any numbers off the top of my head.
Some places were more Orthodox than others.
For example, in Western Europe the rule of thumb is generally that the Jews weren't particularly Orthodox. There were always some (all of the communities had basically started out that way...) but the emancipation and the Reform movement really shrank the size of the Orthodox community. So on the one hand, there weren't a lot of Orthodox Jews there, and these countries were definitely affected. On the other hand, in Germany in particular, the Jews were much more likely to be able to leave the country before the Holocaust actually began- so many many Jews would have experienced anti-Jewish legislation or maybe even Kristallnacht but then may have had the opportunity to leave. So while you get a big proportion of non-religious Jews in these countries, you also get the fact that many of them weren't killed.
Poland and Lithuania/Latvia are interesting, because they had huge Orthodox communities but they also had urban centers of the haskalah, or Jewish enlightenment. (For reference, the haskalah in Eastern Europe occurred about 100 years after its non-Jewish Western European equivalent.) There were many many families with very devout parents and children who were more modern and either less devout or not so at all. There were also a lot of people sort of in between- very linked to their Orthodox families and maybe even with some religious tendencies but with no problem ACTING modern and fudging a bit on observance in a way which would have scandalized their ultra-religious family members. (Just because I was reading it last week, I would refer you to Maus- an amazing book if you haven't read it- and the descriptions of his parents' families.) It made a big difference as well whether you were in the big city (like Warsaw or Vilna, which would have had big communities both of the Orthodox and of the various types of non/not-necessarily-Orthodox, like the Zionists and Bundists) or in the country (like Galicia and other rural areas, where people generally would have stayed religious). Another factor is that for about 50 years, from about 1881-1923, several million Jews left Europe to America- starting with pogroms in Russia and ending with the passing of an immigration bill targeted at reducing immigration, partially with a focus on preventing Jewish immigration. However, while Jews of all kinds came to the US, religious Jews were less likely to go, or at least to want to go- rabbis spoke at length against the excesses and religious licentiousness of America and how it would destroy Jewish practice and religious faith, which strongly dissuaded many Orthodox Jews from going. (My own great-grandfather, who was religious and ended up remaining so, was ostracized by his grandfather when he revealed his plans to travel to America.) As it happens, the rabbis weren't exactly wrong about the problems which the US would cause for Jewish faith, but these warnings prevented a lot of Orthodox Jews from leaving the country. A similar thing happened with Zionism- relatively few Orthodox Jews went to Palestine before the war because the Orthodox Jews were very often anti/aZionist, and therefore they didn't leave. So reasonable guesstimation would assume that large proportions of Jews in Poland/Lithuania/Latvia were Orthodox.
Hungary/Romania had HUGE proportions of Orthodox. While it's true that there were large Neolog (Reform) congregations in big cities like Budapest, the vast majority of Hungarian Jews were very religiously insular. So it's very reasonable to assume that the pretty decent majority of Hungarian Jews killed in the Holocaust were Orthodox.
I'm not super knowledgeable about the composition of religious communities in the Balkans, Italy, Greece, North Africa, etc, but they tended to have large communities both of very modernized Jews and very traditional ones. I don't have enough of a background to make a guesstimate.
Overall, a lot more Orthodox Jews than people think were killed. It's something that a lot of people don't think about, for a variety of reasons. These are the ones I think are significant:
-people focus on the idea of Hitler's ideology as being race-based and not religiously based. This isn't wrong, but a) parts of Mein Kampf do very much express hatred for the more traditional-looking Jews and b) it emphasizes much more the more "normal" seeming Jews, in a "never again" kind of way. The fact that people emphasize Anne Frank, for example, as opposed to a diary of an Orthodox child (and there are several), is at least in part due to a desire to universalize the story- and if you compare the diary with the George Stevens movie, it is VERY VERY obvious, because even though Anne wasn't Orthodox, even those relatively few Judaism-centered portions of her diary were quite toned down in favor of more universalist messaging. By focusing on non-Orthodox victims, you focus on the ones who are more "typical," not "exotic." That lends greater cachet to the whole "irrational hatred" thing.

• as mentioned, more non-Orthodox survived, both in the sense that they survived as a proportion of world Jewry (including those who made it away from Europe long before the Nazis even came to power) and that they survived the Holocaust itself (generally by leaving pre-Holocaust but post-Nazi ascension). Non-Orthodox Jews ended up more likely to be the face of testimony and to be the face of the resistance movements, such as the Warsaw Ghetto Uprising. Some Orthodox Jewish survivors were no longer Orthodox by the end of the war, when they were telling their stories- Elie Wiesel is a good example.
  -those Orthodox Jews who survived tended to keep to themselves in Orthodox communities. As mentioned, they wouldn't necessarily be the ones to tell their stories, and since Orthodox Jews tend to live among other Orthodox Jews, they weren't necessarily spreading out among the population and raising awareness of their presence. You go to certain neighborhoods of New York and you'll still see some quite large communities of Orthodox Holocaust survivors- mostly from Hungary (as they were only under Nazi rule for about a year- there were very few survivors from Poland and Lithuania). But they're not really vocal or obvious.
  While I know I didn't provide much in the way of actual statistics or even approximate percentages, I hope that this provided some help in just getting the lay of the land!