The response of mbloch is perfect. I just want to quote 2 statements taken out from Gemara Avoda Zara 75B (I elided everything not directly concerned with the question)
כלי סעודה אמורין בפרשה
2. דברים שנשתמש בהן ע''י צונן כגון כוסות וקתוניות וצלוחיות מדיחן ומטבילן והם טהורין
 utensils connected with a meal (Soncino's translation).Rashi explains that from the verse that talk about "anything that comes into contact with fire" we learn that only dishes and cutlery are taken into account. The sentence ending is "then it will be purified" talks about Tevila in Kosher Mikve and immediately the purity is raised.
 Used ustensils used with cold meal simply need rinsing with water and Tvila.
So, corkscrews are not cutlery, and do not need Tevila; they may be in contact with cold wine, but only slightly, so at most should be washed