Moses is concerned that the people won't believe that the Lord appeared to him. This is clear from the answer that God gives with his instructions:
[First sign] “so that they may believe that the Lord, the God of their ancestors, the God of Abraham, the God of Isaac, and the God of Jacob, has appeared to you ... [second sign]. If they will not believe you or heed the first sign, they may believe the second sign. If they will not believe even these two signs or heed you, ... [third sign]” (Exodus 4:5,8-9, NRSV)
So all three of the signs were meant to convince the people, not Pharaoh. And indeed, Moses performed the signs in front of the people, and they believed (4:30-31). Moses then appears before Pharaoh without performing any sign (5:1).
Performing signs for Pharaoh doesn't become a concern until later. Two of the signs for the nation (the snake and the blood) are later repeated for Pharaoh, but the original instruction in Exodus 4 was to perform the signs for the nation, and Moses doesn't perform the same signs before Pharaoh until he is instructed to do so (Exodus 7:9, 14-18).