It looks like you already did that so I am going to assume that the file conversion was successful and not corrupted. Flash SWF is the best video format to use in website design so you will need to convert the MOV file to an SWF file.
The QuickTime MOV format is gigantic and is not a good format to use in website design. The default exported format appears to be QuickTime for this program, but the EVR program does offer other formats that you can choose.
I’m going to assume this is the correct program you are talking about because you mention recording your computer screen and inserting the video file into what I also will assume is going to be a web page if you are using Dreamweaver. I see that there is a video recording program called Easy Video Recorder for Mac.