colouring the ring
I'm not sure if this would work with the ring, as it involves running a low voltage through it, but I thought I would mention it as a way of colouring the titanium.
You can anodize your ring with just a couple 9 volt batteries hooked in series, a couple wires, some water with some Tri-Sodium Phosphate (TSP) dissolved in it and a rag or q-tip. Hook one wire to the ring and the other to the q-tip, dip the end of the q-tip into the TSP solution and touch it to your ring. Different voltages bring out different colours.
This idea isn't one I came up with its from Chad Mueller who did a kickstarter for a flat packing camping stove and one of the options is a titanium one and this was a tip if you want to colour your stove. I thought it might be of interest.