Thank you for your question on hiding a feature image from a post. I tested on my own site and was able to hide the featured image on a post and still allow it to display in my facebook share.
I implemented a plugin named ‘Hide Featured Image‘ which allows you to set a featured image, but toggle it to not display. The social sharing plugin I used, Mashshare then scraped that image to use on Facebook.
I am not sure which plugin you are using for social sharing, so I cannot speak for its performance. I also do not specifically endorse Mashshare, it was just a plugin I tested for your question, but using those two plugins I was able to accomplish what I think you were asking for.