Using soft apples to make apple juice
It's not going to hurt anything. The apples they use for cider are usually pretty rough, so a little wrinkling isn't going cause a health issue. You very well may not get as much juice, but the juice you will get will be more concentrated. 

The same principle applies to grapes used for wine...Ideally they will get very little water in the weeks leading up to harvest, so you'll get all the good sugars and flavours, and less of the undesirable water.