I don't think there's a way to do that and gain the same privacy you would (without any on-chain connection). There are solutions which improve your privacy non-centrally, such as JoinMarket, but the inputs and the outputs have an on-chain connection.

I'd be appreciated if you explained how could this work, but as far as I can tell it's impossible unless we entangled it with the Lightning Network which would then create other kind of problems (such as liquidity).