**Since baptizo already implies the use of water.**
Not necessarily. Jesus had already been baptized in water when he said this.
Matthew 20:22
But Jesus answered and said, Ye know not what ye ask. Are ye able to drink of the cup that I shall drink of, and to be baptized with the baptism that I am baptized with? They say unto him, We are able.
And this.
Luke 12:50
But I have a baptism to be baptized with; and how am I straitened till it be accomplished!
These are obviously NOT water baptism.
The word baptizo, in and of itself, implies the use of water, or at least a liquid I suppose. There are certainly some times where it is used as a washing in a figurative sense, such as the two verses you cited, to be sure. But if the ordinary use of the word makes sense in the context, and so using it harmonizes with the rest of scripture, there is no reason to think that it isn’t being used literally. PARTICULARLY when the text is prescriptive - that is, it is teaching for the reader, as opposed to narration.