No way for anyone here to really say. Try this - put some soda (Pepsi, Coke, what ever) into one of your bottles and cap it. Then shake the heck out of it to see if it leaks. This is what I do with any cap/bottle combo that I am not sure about. If the cork has dried out too much to be a good seal, you will know pretty quick.
I don't recommend opening a well shaken bottle but if you are feeling adventurous, well, it's your house!