There's no way in h*ll I would ever give my SS# just to have something shipped. That's just nuts.
I just bought (in August) a few models directly from Stuart Models in Dorset and they used TNT Express to ship to the USA. This package was delivered on a FedEX truck. No VAT, no SS #.
A few years ago I bought some items from ArcEuroTrade of Leiceister. Same deal and they used FedEx as well.
Also bought many bits and bobs over the years sent through the Royal Mail. Again, no VAT, no SS #.
They need to find another shipper.