No, FLVs will not play by themselves, but the code and components to make an SWF that will play an FLV is rather small and not to difficult. I'm sure there are a few out there, but you would likely need to modify them to play your FLV unless someone had one that was using an XML file to feed it the FLV path.
Assuming you have Flash MX2004 or Flash 8, you can go to http://www.gotoandlearn.com and go through Lee's Flash Video Tutorials (start at Flash Video Basics 1 and continue through Video Basics 2,3,4,5 etc until you have all the functions you need). You will have your FLV up and running in no time.
I'm wondering why you're sayng that you have an SWF that is too large to play on your site. Does the SWF have the video embedded into it? If so, you don't need to embed the video, that's the joy of FLVs is they can be external files and play through progressive downloads, which doesn't work nearly as well if the video is embedded into the SWF.