The best way to deploy video on the web is using Flash - it's much easier to embed cleanly into a web page and will play on more or less any browser and platform combination. The only reason to use Windows Media Player is if you're streaming content and you need extraordinarily strong digital rights management, and even then providers are now starting to use Flash even for these. See BBC's iPlayer for a superb example.
I would suggest that you switch to Flash even for internal use. You never know who is going to need to access it in the future, and this will give you the best possible future compatibility.
EDIT - March 20 2013. Interesting how these old questions resurface from time to time! How different the world is today and how dated this all seems. I would not recommend a Flash only route today by any means - best practice these days would probably be to use HTML 5 to embed H264 encoded video, with a Flash fallback as described here: http://diveintohtml5.info/video.html