If it's Ivory the pin test will not hurt it, if it's plastic no harm no foul. Old ivory will yellow with age, and show some cracks, it looks to smooth to me to be Ivory, but as stated it's hard to tell from a pic, nice find either way.
Just a thought, It is a cork screw, no doubt there, the steel has to be well bonded to the handle or it would never work, Look to see if It goes all the way threw and was capped over, If its plastic the steel should T off inside the handle to make it strong enough to open a bottle of wine.
Look very close where the screw joins the handle, If it is plastic There should be some trace of a seam.
Also a drop of lemon juice on the steel will tell you if it is carbon or stainless, that should help to date it .
It looks to be carbon but I cant say for sure.
My best guess is that it is Greek 1910 -1940