If you don't particularly care that the document ends up using the same exact style as you used before, you can pick whatever style you want and all existing citations will be adjusted accordingly. That's assuming that the existing citations have not been turned into plain text. You can check by placing your cursor in a citation and clicking Edit Citation.

I don't think there's currently a convenient way to see an existing style if this style is not installed on the computer. Zotero should definitely do this and offer to download the style (I've run into this issue as well actually). There is a way to check this, but it may depend on which word processor you are using and which version.

As an example, in Word 2010, you can click on the File tab -> Info -> (right-hand pane) click Properties label -> Advanced Properties -> Custom tab -> click on each ZOTERO_PREF_# and copy the contents of the "Value" field to a text document (don't separate by newlines or anything else). This will reassemble Zotero properties for that document in an XML format. What you're looking for will be something like <style id="http://www.zotero.org/styles/cell" ...