"And he drew out his hand" means: he took it out from the collar/opening of his shirt.

Al-Kalbi said:

It has reached us that Moses said: "O Pharaoh, what is this in my hand?" He replied: "It is a staff." Then Moses cast it down, and suddenly it was a manifest serpent that filled the house with its sheer size. It then lunged toward Pharaoh to swallow him, so he cried out: "O Moses, O Moses!" Moses took hold of its tail, and it became a staff in his hand once again. Pharaoh then said: "O Moses, is there any sign other than this?" He said: "Yes." He asked: "What is it?" He said: So Moses brought out his hand and said: "What is this, O Pharaoh?" He replied: "This is your hand." Then Moses inserted it into his shirt pocket and brought it out, and it was white for the observers; meaning: it dazzles the vision with its whiteness.