You answered my question, but used what xins wrote. It seems you are getting confused. As for not relying on works to get to Heaven, that is true when you are talking about meritorious works, or works of the flesh. However, many denominations belief that confession and repentance are required for salvation, as do I, but they don't consider them works. Yet, they consider baptism a work, because it doesn't fit in their denominational doctrine. Baptism is no more of a work than confession or repentance, and actually is less of one, since the work is being done by the baptizer and God.
As I said way back when, I believe baptism is extremely important. It is a sacrament of the church instituted by Christ. I believe the Holy Spirit lays it on every true believers heart to become baptized and it is part of our salvation story.
It is a work, but a work bearing good fruit which come from God's moving us by His Holy Spirit. I've never met a professing Christian who didn't want to be baptized. Those who claim to be Christians but don't wish to be baptized are suspect and I have met plenty of people who were baptized and renounced the faith.
I don't believe baptism is what regenerates you for regeneration occurs before baptism. Like Cornelius people WANT to be baptized because they believe. They don't pop up from the water and then believe. I don't know how much plainer this could be.