Karaoke Bar? In Japan? You must speak Japanese well enough to pass genuine Japanese bar girls out there. If you don't care where they are from, you may speak in English to Chinese, Russian, Filipina and/or Korean etc. foreigners bar girls there.
In addition, you need to consider to pay quite expensive charge even for just one set no matter how many girls you designate. If you just want to sing songs, go to Karaoke room where you can drink either. It costs much cheaper.
If you meant to be the family type Karaoke room, that is usually providing a separated room for each customer group so that you don't worry about any reaction from others unknown.
Many bars in Japan have their Karaoke service and locals down there don't care who sings songs anyway.