I'd go for @Muppetteer's route but turn down Oakley Street onto Albert Bridge before picking up the Thames Path towards Wandsworth. Take care on the south side of Albert Bridge as people tend to try to squeeze past at the traffic island.
You can also nip down Pond Place and turn right-left to get onto Sydney Street (or even Cale Street > Dovehouse Street), but that's a very minor bit of route optimisation to get on the quietest streets.
I'd go for @Muppetteer's route but turn down Oakley Street onto Albert Bridge before picking up the Thames Path towards Wandsworth. Take care on the south side of Albert Bridge as people tend to try to squeeze past at the traffic island.
You can also nip down Pond Place and turn right-left to get onto Sydney Street (or even Cale Street > Dovehouse Street), but that's a very minor bit of route optimisation to get on the quietest streets.