You're very wise to be cautious, but if the company is legitimate, it's okay. That said, if an application gives me the option to defer submitting that information, or allows me to put in something like 124-56-7890, etc., I will sometimes do that initially, especially if it's a company with which my familiarity is limited.
At some point, however, you will have to submit it to be paid, and some companies do require a legitimate number before you can shop.