First off, do you/they care about the color?
If you do, then I would use some lexol leather conditioner, or some bick 4. Both will renew the leather and make it resist water without darkening it any.Just soak as much in as you can.
If you don't care about color. I would use neatsfoot oil. This would be a more long term fix. It is made out of the natural oils that are in leather to begin with. Its pretty thin and will really penetrate the handle. I put it on my work boots to make them more water proof and it lasts about a year.
Both ways will soften the handle and make it more grippy than dried out slippery leather.Leaving it dry will lead to it cracking and falling apart too.
------------------
Fix it right the first time, use Baling Wire !