Just an idea, like
Why don't the BBC get to work CGIing some famous types (Freddie Starr, Jim Davidson, Jimmy Tarbuck etc.) to deliver the original announcements but replace the convicted pervs on old TOTP footage?
Joking aside, it's bloody ridiculous that they haven't been showing the old TOTPs because of the presence of these blokes. (Personally I, along with all my friends, found Savile offensive back in the 60s and 70s, but they still showed him regardless.) Why this sudden compulsion to expunge all these people from history? I remember they even cast a convicted murderer in a lead role in one of their most popular soaps. What hypocrisy.
At the very least they could just edit out the links from the affected programmes. TOTP2 was produced using captions only. Surely it would only be a couple of days work for some junior BBC editing assistant. The repeats of TOTP are usually edited anyway - the early evening one tends to have a couple of songs cut out to fit into a 30 minute slot. The late night repeat is complete.