I use a DVD-CDG player myself for singers own disks there are plenty on the market, mine is a Bluelasser DVG-888u Karaoke player. I use this one as it is only 1U in height and fits in my rack but there are plenty to choose from. I use a video-audio switcher to swich from computer to player.
An example switcher is shown here:
http://www.acekaraoke.com/audio-2000...-selector.html
I don't personally use this one but it would do the job for you.
The one I use can be seen here but this is an English Site:
http://www.maplin.co.uk/Module.aspx?ModuleNo=32114
I have on order for myself a new mixer from Vocopro, Model KJ-7808RV as that has video fader mixer built in but as I am from England not many people sell it and those that do are out of stock, I have been waiting about 6 weeks now.
Yes it does mean carrying more equipment with you.