Simple.
I can prove scripture does not say Naaman entered into or agreed to a covenant because no scripture states he did.
Which is irrelevant. Salvation is not a function of choice.
No scripture states it is. You've just refuted your original position. Instead of making inferences based on what scriptures does
not say, try accepting and believing what scripture does state.
Ephesians 2:8
For by grace you have been saved through faith; and that not of yourselves, it is the gift of God...
For by grace Naaman was saved through faith, and not of Naaman's self.
Acts 4:12
And there is salvation in no one else; for there is no other name under heaven that has been given among mankind by which we must be saved.
If Naaman was saved from sin and wrath
(and not just leprosy), then he was saved by the name of Jesus Christ the Nazarene.
John 6:44
No one can come to me unless the Father who sent me draws him; and I will raise him up on the last day.
If Naaman was saved from sin, then he was dragged like a fisherman hauling a net out of water to Jesus, the only name by which he could ever possibly be saved.
If Naaman was saved from sin, then it was when the little girl from Israel was captured that God began to work in Naaman and Naaman was oblivious to that fact. God saw fit to have a little girl captured and brought to his house to tell him of Elisha. We might even say he was struck with leprosy for the purpose of bring the knowledge of God to Babylon because God never acts fruitlessly, nor without purpose. Like everyone else in scripture, the man had to be broken. All his pride, anger, and preconceived notions had to be stripped from him? Why? Because choice does not save. It is
knowledge, not faith, that causes a person to say, "
Behold now, I know that there is no God in all the earth, except in Israel." He did not believe it. He knew it. It's very much like getting knocked off one's donkey, being struck blind, and hearing a voice from the sky state "
I am Jesus, who you are persecuting,"

or having one's hip broken or hearing and seeing a speaking bush that's on fire but does not burn.
If Naaman was saved, then it is only through the promises made to Christ that he got that way. If scripture never states Naaman never entered into a covenant, then maybe he was not a covenant member, and you should not think he was. Likewise, if scripture never states Naaman made a choice to be saved from sin then maybe he did not make such a choice, and you should not think he did.
There were many lepers in Israel in the time of the prophet Elisha, and none of them was cleansed, but only Naaman the Syrian.