If you give someone a Form 1099-MISC, then yes you will need their Social Security Number.
You are only required to give someone a Form 1099-MISC if you paid them $600 or more. If you paid that individual less than $600 you do not have to give them Form 1099-MISC but you can still take the deduction for what you paid them.
If you did pay one person $600 or more and you deduct this on your tax return without giving that worker a Form 1099-MISC, the IRS will ask you why you didn't.
