Hi Joe -
Are these factories located overseas or here in the US? Either way, it is always wise to request that anyone sign a non-disclosure so that you have documented proof that someone has agreed to not share your product idea with others. That said, some factories and most retailers will not sign NDA's. This is a gut call...if the factory refuses to sign an NDA you may choose to move on. There will always be risks and even with an NDA it may be tough to enforce and the cost of doing so with attorneys can get expensive.
You are certainly correct to feel uneasy! If you feel uncertain, just find someone else you feel has the integrity and experience to help you and make you feel comfortable...
Jim
www.jimdebetta.com