I know it's something to be concerned about doing. I had my doubts about giving my SS number too. Someone suggested using 999-99-9999 and I have done that for several companies. But once they offer you shops you have to go into your profile and make the change for your W9. It's one way to be sure the company is legit before you commit to giving your real SS number. They have to have your correct SS number or you won't be paid.
I'm really fond of the companies who send you to their site to print or send you an email with the W9 attached. Then you print and fax the W9. And the contractors agreement. Fill them both out yourself. They don't all do it but most do from my experience.