Your thesis is that because there is no record in Scripture of Jesus Christ using a particular Greek word that you arbitrarily chose.
Please look at what Scripture actually says:
John 21:25 Now there are also many other things that Jesus did. Were every one of them to be written, I suppose that the world itself could not contain the books that would be written.
Yours is an argument from silence, and silence proves nothing other than silence itself. In other words, it is logically impossible to say that an absence of evidence is actually evidence of anything. By definition, silence is a void from which nothing positive can be deduced.
Secondly, you are mixing human beliefs with Divine attributes. Being fully God, and with the exception of His second coming, Jesus knows everything there is to know about the beginning and the end. He calls Himself "The alpha and omega" and states that He alone is the gateway into heaven:
John 14:
6 Jesus said to him, “I am the way, and the truth, and the life. No one comes to the Father except through me.
7 If you had known me, you would have known my Father also. From now on you do know him and have seen him.”
8 Philip said to him, “Lord, show us the Father, and it is enough for us.”
9 Jesus said to him, “Have I been with you so long, and you still do not know me, Philip? Whoever has seen me has seen the Father. How can you say, ‘Show us the Father’?
10 Do you not believe that I am in the Father and the Father is in me? The words that I say to you I do not speak on my own authority, but the Father who dwells in me does his works.
11 Believe me that I am in the Father and the Father is in me, or else believe on account of the works themselves.
As a result, it is not being wrong or snarky to state that while your intentions are good, the result is that you are conflating the need for humans to have faith in Jesus Christ and the fact that Jesus Christ is the Guarantor of our entrance into heaven. That is because He alone is both 100% God, and 100% human. One Divine Person, having TWO distinct natures, neither of them being confused, nor mixed up.