You can connect (if available) the s-video out to the video or TV, and if possible (most laptops come with this) a VGA/DVI output. This all depends very much on what connections are available on both laptop and VCR/TV.
Another downside will be having to connect your laptops souncard up to an external amplifier, and then you've got to consider your microphone.
You may also find you'll have problems with Macrovision, which is a technology designed to prevent copying, especially if the Karaoke is to be played from disk.
All in all your probably better off buying a cheap karaoke system and routing it through a decent amplifier or surround sound system.