Private Tour - Tower of London

Sorry, can't help you with a private guide but I think you'd be missing something if you didn't take the free Yeoman Warder's tour that comes with your entry ticket. These esteemed armed-forces veterans and their families live within the walls of the Tower, and their generally hour-long walk-and-talks are interesting, fun and altogether a great introduction to this former fortress/prison/palace with a 1000 year-old history. Please consider?

https://www.hrp.org.uk/tower-of-london/whats-on/yeoman-warder-tours/#gs.ke4dyj

You might also explore some of the exclusive, paid tours on offer, although they are VERY expensive:
https://www.hrp.org.uk/tower-of-london/hire-a-venue/private-tours/#gs.ke4huo

Note as well that booking advance tickets for a particular date/time slot alleviates standing in long ticket lines, and the security-check queue can't be avoided.

https://www.hrp.org.uk/tower-of-london/visit/tickets-and-prices/#gs.ke4m3a

Editing to add: I've not taken this tour but Context has gotten high marks on these forums from visitors who've taken their tours in various European locations. You might look at booking their private 3-hour tour for 2 of the tower?
https://www.contexttravel.com/cities/london/tours/tower-of-london-tour?display_currency=USD&search_started=true&showcase_ids%5B%5D=65

Also check with Blue Badge Guides:
https://britainsbestguides.org/tour/tower-of-london/

You can’t get past the security line.