Does shortbread ship well?
Shortbread ships well, especially if you make the individual biscuits fairly thick.  Walker's should be your guide here: theirs are about 0.75 to 1cm thick, which helps prevent crumbling in transit.  Shipping them in a tin is also advised.

Shortbread is also fairly shelf-stable.  Freshness time depends on storage conditions, of course, but below 75F they should be good for one to two weeks.