Private tour company in Prague

Yes. I have used The Naked Tour Guide when I was in Prague. It is run by Martin Bradshaw.
He is Irish but has lived in Prague for quite a while. www.nakedtourguideprague.com. We did the early morning breakfast tour and loved it. Enjoy Prague!

I would recommend you check out the itinerary of some of the tour guides carefully. Some of them only take you to the Charles Bridge, Jewish Quarter area, Old Town Square and Wenceslas Square. These are easy to walk to and really don't warrant the prices they charge because most all of these have no entry fee. You could do these all on your own with an audio guide or a little reading prior to your trip. I think Rick Steves has a free audio guide of Prague for free. http://podcasts.ricksteves.com/walkingtours/prague-city-walk.mp3

just to correct Pat's answer it is Marcus not Martin. lovely guy and though Naked tours are a small group tour company they will do private tours if they can .Marcus sometime comes on the forum to offer his help
https://livingprague.com/tours/living-prague-tours/
this is another small group tour company that will also do private tours if asked and can fit them in.
Run by Jason who also comes on this forum fairly regularly, nice guy too.

Thanks for the recommendation. I've just sent a PM to the OP.