I used mineral oil to revive the strops on the back of a couple of razor hones. Both of them were extremely dry, but just a small amount of the mineral oil rubbed into each made them soft again.

Admittedly, both were extremely dry, but the leather hadn't become brittle yet. I'm guessing that as long as you apply it sparingly it shouldn't be a problem. Once the oil has softened the leather you can continue the process with the oils from your palms alone.