Well, first you write the first draft. Then you rewrite it several times before you have a finished story. (And then you submit it, and if it gets accepted you rewrite several more times...)
The first draft is not the final product, and how you write it depends on what you need to get it done.
Lots of authors write their stories in another order than the chapter order. And then many other authors create books where the chapters aren't in chronological order.
For instance, I try to write in chapter order and keep the chapters in chronological order. I sometimes still have to go back and add to the text when I need a character, or character development, or something else. And then, in the rewriting, I usually have to do even more with it.
If you feel that writing the chapters out of order is a problem, is it a problem that prevents you from writing the next chapter, or is it a problem that you feel that you "should" write the chapters in order?
It's only if it prevents you from writing that it's really a problem.
That being said. Research is important. Not only will it prevent you from adding elements to your novel that will sound strange or untrue, but it can also offer lots of input and ideas.
I think historical fiction is a bit like my genre (sci-fi) in that the research is needed to avoid physically impossible ringworlds, teleporting in the wrong direction, and any number of inconsistencies in history (I can only imagine having an actual source to what actually happened would make any errors seem even more glaring...)
You don't mention why you've started writing while feeling you lack research or why you can't get at it, but while you certainly can keep writing, you obviously need to have all the research in place before you can really call the book (or even the first draft?) finished.
Even though I have most of my research in place I sometimes get myself into places where I've created some situation that doesn't work. It's like; if he's going to do this, and she's going to do that then... all these things can't happen... oh well... back to the drawing board...
I'd probably get even more "oh well"-moments with less research, less world-building, and less character-building...
I can imagine someone using a tool that hadn't been invented or referring to some event that hadn't happened might be a small problem... or a show stopper... Regardless, it will likely force you to do more rewrites or fix more problems...
So, even if it doesn't prevent you from writing... you should probably try to get the research in place first. But if you can't do that, keep going, but expect more rewriting and problem shooting...