The risk isn't necessarily to us. I would say putting on a powerful sentient magical item is more risky for the girls than for Hunger.For curious parties, I dug up the Word of Rihaku that giving the Ring to Gisena or Letrezia is possible.
A Simple Transaction I Original
A quest about a simple transaction and the consequences that follow.forums.sufficientvelocity.com
If giving the ring to Gisena or Letrezia is enough to give them the potential to be a threat to US? Then you combine that with Philosopher's Wreath, or Ennoblement, or Ruling Ring fueled boost X? The long term viability of associating with one of them goes up. WAY UP.
Edit: Not that I'm against giving them the Ring.