I asked a jeweler about resizing a ring down to a smaller size, especially given the delicate nature of this ring. She had two recommendations: a bridge (which may not require any soldering) and beads.
A bridge is merely a piece of metal that kind of wraps around the inside of the ring to add additional material, thus causing the ring to fit better. Some bridges can be soldered to the ring, others are simply wrapped around the material and are not permanent. Her recommendation was to obviously use the non-permanent bridge to avoid damaging the outer protective layer. It would work something like this:
Her other recommendation was the beads. These are little balls that are soldered to the inside of the ring to, again, take up more room, thus making the ring feel tighter. She says that due to the spot soldering, it would likely not damage the inlays (she thinks) or the outer protective layer. Of course this is risky because we don't really know how much short-term direct heat the inlays can take from a soldering job like that. Her recommendation for beads is to solder them directly underneath the non-inlay parts of the ring, to prevent possible damage to the inlays. It would work something like this: