From previous experience, I would suggest you not engrave deeply on something that has super glue in or on it. Heating the glue releases cyanide gas. In small amounts, it’s not enough to hurt you, but it can damage your optics and causes other issues with machine parts.
I’m curious about whether or not you were able to make your rings with wood glue? I imagine it would take longer for the dry time and require a slightly different method to wrap it until dry.
That is gorgeous! Be sure to show us more when you try the inlay.
Your ring is stunning. I especially like the contrast between the wood and the coin. Thank you for sharing your design. 
I was thinking about engraving the wood veneer before the glue is added. I don’t think wood glue wood be a good choice since it is a thicker glue & kind of cloudy. Might be interesting to try it though.
I think you misunderstood my intention. I don’t intend to lase super glue.
Also, I haven’t made these rings; it is someone else’s video.
I agree about the transparency of wood glue. Years ago I wiped super glue off of a finger on a piece of wood. couldnt help but notice the wetting finish it gave , and hard.