Bronco,
When used as an electrical contact, I would imagine that electrical conductivity and corrosion resistance would be most important. And these two characteristics are usually better in lower strength, more ductile metal alloys.
Structural rivets are primarily designed to take shear loads. So shear strength is usually of concern. But there is a compromise between shear strength and ductility. Since rivets must usually be cold worked at installation, having the portion of the rivet body that will be upset ductile is of some benefit. It will be easier to install and less prone to cracking. The cold working when the rivet is upset can also sometimes improve the strength of the rivet with alloys that tend to work harden.
If your concerns are purely manufacturability of the rivet itself, then choose an alloy and heat treat condition that gives the highest rate and yield for your particular production process. For example, if the rivet is machined, this might be a free-machining alloy.
Hope that helps.
Terry