Google Docs? LibreOffice? Just make it simple, if they are about box ticking then it does not matter at all how well your resume looks (as e.g. a PDF version would).
I mean I feel your pain, Word Docs give me the cold shivers, but there are some tools.
Word doesn't produce a document that looks exactly like the document you created unless only open and view that document on the same version of word you created it on. Everyone, even HR/business types, inherently know this from their years of dealing with Word.
In short, if your format messes up a little bit no one cares.
And yet, having your format messed up is completely unnecessary. We have this format called PDF which exists solely to make the same document look the same for everybody. It works on every major platform and is supposed by lots of software.
Unless the HR department intends to edit your resume, why on earth wouldn't they accept PDF?
I mean I feel your pain, Word Docs give me the cold shivers, but there are some tools.