Is there any reason why this could not be translated: "我们要不要旅游签证"?
In that case, it should be"需要不需要"。 Because"要不要" means: "do you want it or not". 需要 actually means: "need"。
要 can also mean need, but I agree that 需要 is better for clarity.
”我们需不需要旅游签证” should also be correct, however it only accepted: 我们需要。。。吗