All parts I've seen up to now in electric engineering use thin metal. Good elastic properties and conductivity are obtained from copper slightly alloyed with Cr, Ni o Be, and where possible cold rolled for hardness. If the contact quality matters, the parts must be gold-plated.
A few polymers are conductors, not as good as metals, and I haven't heard of an elastomer - is there one?
Sometimes graphite nanopowder is mixed with an elastomer, but this makes an on-off contact as the elastomer deforms. This is desired to make keybords contacts, more reliable than metal-to-metal contacts. The resistance varies then in the kiloohm range, not milli nor microohm.
Can you replace your function by an insulating elastomer and a separate contact?
Making switches, connectors and moving contacts (in case that's your intention) is a special job, only for trained people at specialized companies. It's just like seal rings: buy them, don't try to make them by yourself.