Quickly converting Scrivener’s non-stylesheet output to stylesheets in Word is quite easy, and I’d say beneficial, as a document with stylesheets in Word is going to be more useful than one that is just loosely formatted. At the very least, you can use the Navigation sidebar to get around in the headings. But that’s also how you can easily make a ToC, or change the style of the document with a few clicks.
So the way you do it in Scrivener is exactly how nom suggests. The important thing is consistency, not accuracy. In fact, being wildly inaccurate can sometimes be easier for you than close to accurate. What I mean by that is: if your section headings are bright green and your sub-section headings are bright red, you can very easily find them and it is obvious which is which. Not so much if one is 18pt the other is 16pt. That’s a bit of an exaggerated example, but the key thing to take from the example is that you don’t have to be making something that looks almost right, or even 99% right in Scrivener. The important thing is that all sub-sections are identical. If you use the Formatting compile option pane to set your headers for you, based on the binder titles, then this is all cake that you can have and eat (and you don’t have to stare at bright red text in your window).
In Word, all you need to do is find an example of something to convert to stylesheets, right-click on it, and go into the “Styles” section of the contextual menu. Don’t be distracted by all of the fancy graphics, you don’t want to actually choose a style yet, that will just change this one single spot. Instead, toward the bottom, use “Select All Text with Similar Formatting”. You may not be able to see it, but every single bit of text in the manuscript that looks like the thing you right-clicked on is now selected. Now click on a style in the ribbon that matches what you are trying to do. “Normal” for the main body text, “Heading 1” for the main sub-division like Part or Chapter, “Quotes” and so on. The average document is only going to have a handful of formatting variations, so this shouldn’t take too long. I agree with Nom, this is a twenty minute (if that) thing you can do to dramatically boost how useful your final output is to everyone down the line as well as yourself.
Note, I’m basing my instructions on Office 2010 for PC. I’m guessing Mac 2011 is similar, but I can’t say what the process would be for older versions of Office. I do know this has been possible for many years, so a little Google should be helpful if these instructions do not match.