I doubt that you could delete Safari, itself, without an uninstaller, and as far as I know, none exists, but deleting its "support" files, restarting, and installing a new version of Safari over your old one would be a useful exercise. (ganbustein has shot down the venerable troubleshooting step of trashing plists, though, so I'm not certain that simply deleting yours will be effective.)
But it may make a confounding issue go away and deprive all present of the joy of head-scratching.
