Shipping cost assigned to single product

I've got my shipping set up pretty much the way I want it with one exception. We have one small item (a lapel pin) for which our existing site says:

No extra shipping charge if included with any book order. Shipped separately, add $1 shipping/handling for any quantity from 1 pin to 20 in the same order.

Is there any way to do that? I have several products where the shipping cost is included in the price, and that's working using attributes; so I tried to clone that for this product, using the "flat rate" shipping module, but all that did was put "$1 shipping" as an option on all my products. Either I don't understand how the attributes work or that only works with the free shipping module.

If there's no way to do that, I'll just have to add another zone with a smaller weight cutoff for this...