I am not sure how that is going to work. I assume you are talking about lightning, liquid or a similar protocol. You are still going to need to make an on-chain transaction to join that second-layer mixing protocol and a second transaction to get back full control of your coins and record the changes on the blockchain. Unless you mix regularly, you aren't going to have open channels and routes to whatever nodes you need to connect to perform your off-chain mixing. People who don't mix on a regular basis won't save anything if they don't maintain their LN channels.