I've never used it but it looks like Flash Catcher
would do the job of saving the files from websites.
As for removing the audio and adding your own. Any number of video editing programs should be able to do that. Adobe Premiere Pro and Final Cut can both do it very well (but of course they cost a lot and are overkill for what you want).
Windows Movie Maker can do it as well I believe (and this comes with Windows)