You have to give them your SS# either way. If you're an employee, then you give them a W-4 with your SS# and they issue you a W-2. You'd be responsible for taxes plus the social security and medicare that SHOULD have been withheld all along.
If you're a contractor, then you'd have to give them a W-9 with your SS# and you'd owe taxes plus self employment taxes that cover both the employee and employer half of the payroll taxes.
Either way, you MUST give them your SS# and report the income and pay taxes on it. Legally speaking, you were required to report it whether or not you ever got a tax form. You can dispute your status as a contractor and make your case to be treated as an employee, but you still have to report your income and pay taxes on it. The only thing in question on the contractor vs employee discussion is half of the payroll taxes.