I remember loads of Hanna-Barbera stuff being shown on CBBC well into the 90s. I remember them showing that bizarre Flintstones sketch/variety show from the 70s during the breakfast slot in the late 90s (which would have been better off never beeing seen again!)
I also have on video the last few seconds of a screening of the 50s Felix The Cat cartoons that for whatever reason got repackaged with a new theme tune in the early 90s. Speaking of that I'll also point out The Twisted Tales of Felix The Cat from the 90s- though I think CITV showed that one.
The Flintstones, and its seventies spin-offs, were rarely shown as part of CBBC, though - when they film came out they showed it quite a bit and they might have screened one or two earlier but normally it would be before or after CBBC. For a time they showed it at 6am before Breakfast News, and I remember someone writing into Andi Peters' column in Fast Forward where he answered your TV questions, asking why they'd stopped doing that. I remember him saying that it was actually bought by the Beeb for adult audiences, and it was too expensive to keep showing at 6am to no viewers, so they'd moved it to the 10am slot on Mondays which for the rest of the week was home to the repeat of the previous day's 1.50 quiz.
You're right about the re-edited Felix The Cat shorts in the early nineties, and there was also the Ralph Bakshi revival of Mighty Mouse around the same time. This was a completely new series - which I can see from Wikipedia also showcased the talents of Jon "Ren and Stimpy" Kricfalusi - which I found very enjoyable as a kid, but I remember they also did a couple of episodes using recycled and re-edited footage from the original series, much to my bemusement.