I don't have any knowledge of private guides, but are you aware that the Tower's own Beefeaters (the official name is Yeoman Warders, dating back to the reign of Edward IV (1461-83), not just tour guides but ex-military with at least 22 years service and good conduct) give free tours every half hour?
https://www.hrp.org.uk/tower-of-london/whats-on/yeoman-warder-tours/#gs.9nn55t
They include the Chapel Royal of Saint Peter ad Vincula (where Thomas More, Henry VIII's Lord Chancellor, and John Fisher, the Bishop of Rochester, were executed in 1535 and are buried here. Both are revered as saints of the Catholic Church and are remembered through a dedicated place of worship in the crypt. Most famous however, is the burial of three Queens of England within the Chapel: Anne Boleyn, Catherine Howard and Lady Jane Grey, who were all beheaded at the Tower) to which you are taken by the Beefeater tour.
I hope your private tour works out for you, just check that they can take you to all the places a Beefeater can.
Particularly important is how you will see the Crown Jewels - if they are important to you. They are up by the barracks beyond the White Tower, up the hill. Crowds make their way there shortly after Tower opens and lines form shortly thereafter and remain all day. A private guide won't get you to the front so the best advice is to get there when the Tower opens. You may even have a chance to go through twice if you want, before the lines form. The Crown Jewels are in a somewhat darkened room and you stand on a moving sidewalk which carries you in front of the various jewels, and when you get to the end you go out. Thus the advantage of going through twice. Once the line forms it can be up to an hour or more so the chances of going through twice are gone.
If you don't find a private guide I'd suggest getting to the Tower at or a bit before opening, go straight up to the Crown Jewels, then make your way back to the Middle Drawbridge and pick up a Beefeater tour, and when that finishes you can spend time at all the other wonderful parts of the Tower, including a nice lunch at the very tasty New Armouries Café.
If any of your party have various visible and invisible special needs, if contacted in advance the Tower can arrange special tours taking those needs into account.
I'm a member and frequent visitor and happy to answer other questions.
Sorry I can't help with a private guide.