back to 2ndThermoLaw's post (on the 16th).
an obvious design aspect of using 1097s is their reduced tension capability. i know you're not going to be designing them to carry tension loads, but the issue may arise when you've used them in a thin gauge skin which then buckles (under shear and compression). off the top of my head i don't remember how NACA TN2661 calculates the tension loading on the rivets due to buckles forming, but i think you'll need tension allowables which are going to be hard to find (but they are pretty easy to generate).
regarding planedr's post (back on the 15th), i'd wouldn't put a 1097-5 in 0.036" skin, nor a 426-3, and i'd never describe either as "better fatigue" ... both are going to very limited in fatigue life and i think the 1097-5 with it's higher static allowable might beguile the designer into thinking things are ok. if i had to use a CSK rivet (in 0.036" sheeet, primary structure) i'd opt for a 1097-3, but i'd rather a 470-4.