振る: a signal flag and a silent shake of the head
Read 振る through a waved signal flag and a quiet head movement. Distinguish the ship starting to move from a nonverbal response without inventing a spoken answer or treating every head shake as refusal.
A waved flag signals the ship's movement
振る (ふる) can describe waving an object. 「合図の旗を大きく振ると、船がゆっくり動き出した。」 means “When we waved the signal flag in a wide arc, the ship began moving slowly.” 合図の旗 is what was waved, followed by the ship beginning to move.
合図 identifies the flag movement as a signal. The wide movement of the flag and the ship's slow start are the stated details. This does not establish the ship's destination or the completion of its voyage.
A quiet head shake instead of an answer
「彼はその質問に答えず、静かに首を振った。」 means “He quietly shook his head instead of answering.” 首を identifies what he moved, while 静かに describes the manner. Here the movement belongs to a response to a question rather than to a flag signal.
答えず keeps the scene from providing a spoken reply to that question. Do not invent words such as “I refuse” as something he actually said. A nonverbal response is present, but its precise reason or the meaning of every possible head movement is not fixed.
Find the moving object and whether a reply is stated
The flag sentence presents a signal followed by the ship's movement. The head sentence presents a bodily response instead of an answer to a question. Identify 旗 or 首 as the object of 振る and connect that movement to its particular scene.
Shaking one's head in response to a question is not the same as giving a spoken reply. Preserve the quiet bodily response without adding a sentence that was spoken. This one example also does not make 振る or head shaking an expression of refusal in every situation.
Does 「彼はその質問に答えず、静かに首を振った」 give the words he actually said in reply?
Show the answer and why
No. It describes him quietly shaking his head instead of answering the question. A spoken answer or a refusal meaning that applies to every context should not be added.