Not sure why they would need your SSN. Technically, it is only to be used for social security purposes. Banks, lenders and other financial companies (other than stupid Credit Reporting Agencies) are moving away from the SSN.
Back to your problem. I would not provide them with your SSN, period. I remember buying some Yamaha stereo equipment from Japan and when it was shipped to me, I had to pay the USPS Carrier. In a sense the tariffs/customs was C.O.D. I would call them back and see if you can provide some other type of information or pay the customs fee up from...
How do you get an ITN?
http://www.irs.gov/individuals...#what
IRS wrote:Are ITINs valid for identification?No. ITINs are not valid identification outside the tax system. Since ITINs are strictly for tax processing, IRS does not apply the same standards as agencies that provide genuine identity certification.ITIN applicants are not required to apply in person, and IRS does not further validate the authenticity of identity documents. ITINs do not prove identity outside the Federal tax system, and should not be offered or accepted as identification for non-tax purposes.
So I am not sure why they need an ITN.