If you do not want to give your SSN, I suggest that you get either a TIN (Tax ID Number) or create a corporation for yourself.

Now about SS-4, that is the form to request an Employer Identification Number and you can only use this form if you have a corporation already.

Identity Theft can happen anytime and when you least expect it. If you want to protect yourself, just watch your credit report and finances. While I was going to college I worked for a bank and I had a case of identity theft but the customer was able to get a new Social Security Number and erase all the bad records on her credit report due to identity theft.