Even the WTS says it was just for show:
*** w85 9/15 p. 8 Jesus? Baptism ***
Why is it right for Jesus to be baptized? Because Jesus? baptism is a symbol, not of repentance for sins, but of his presenting himself to do the will of his Father. Jesus was a carpenter, but now the time has come for him to begin the ministry that God sent him to earth to perform.
*** wt chap. 12 pp. 111-112 The Meaning of Your Baptism ***
Among those who came to John to be baptized was Jesus himself. But why? Knowing that Jesus had no sins to confess, John said: "I am the one needing to be baptized by you, and are you coming to me?" But Jesus? baptism was to symbolize something different. So Jesus replied: "Let it be, this time, for in that way it is suitable for us to carry out all that is righteous." (Matthew 3:13-15) Because Jesus was without sin, his baptism did not symbolize repentance over sin; nor did he need to dedicate himself to God, since he was a member of a nation already dedicated to Jehovah. Rather, his baptism at 30 years of age was unique to him, and it symbolized the presenting of himself to his heavenly Father to do His further will. (WTS Italics)