For this, I went with something close to the cartoons of Tex Avery or the Looney Toons shorts from the 1940s.
There's also a little something of 'Animaniacs' here that fits these characters.
In fact, if I'd been in charge of casting this movie I would have hired Rob Paulsen and Tress Macneille to do their voices. If you can imagine Yakko and Dot Warner with Cockney accents, you've about got them.