Both sentences express similar ideas.
HOW and THE WAY (you do something) are interchangeable. But there are word partners, word sequences that we often use together. And such is `I don`t like the way ............. (you do something for example) ` It`s likely that if we start the sentence with `I don`t like ` then we`re gonna continue with `the way` when we want to express this idea.
Your first sentence is perfectly good too though. It sounds more like a suggestion, a good idea.