The command to teach and ritual baptize was given to the Lord's ministers rather than to believers. In point of fact, though Paul was a minister, the Lord didn't commission him to ritual baptize (1Cor 1:17). Were ritual baptism essential to one's safety, as you allege, then the Lord would most certainly have included it in Paul's ministry.
You appear a bit confused - "the Lord's ministers"
were believers and baptism in water was commanded to all who would be disciples of Jesus Christ. The NT does not know of an unbaptized Christian. Why - because all believers were baptized immediately upon their confession that Jesus was the Christ.
Paul's ministry always included baptism in water (a burial) and Paul did baptize some and those who assisted him baptized all of the others.
Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death? Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life.
(Rom 6:3-4)
Paul's words are hard to miss - one is not "in Christ" until one is baptized in water - "baptized into Christ". Paul himself submitted to baptism to have his sins "washed away" by the blood of Christ
at the point of baptism...
And now why are you waiting? Arise and be baptized, and wash away your sins, calling on the name of the Lord.'
(Act 22:16)
You may want to re-think the nature of baptism as presented in Holy Writ.
“He that believeth and is baptized shall be saved...” (Mark 16:16)
"These words are very important. The first clause [belief and baptism] opposes the notion that faith alone is sufficient for salvation, without those works which are the fruit of faith" ~ Pulpit Commentary