For some context here, I am a techie, not a craftsperson of any kind and I have very few tools at home. I have started to get interested in making geometric laser cuts (ordered online) and I was fooling around a little simulating what a pair of coasters could look like made out of two kinds of wood (this shows red oak and black walnut). I could order this and assemble it, but I'm not entirely sure how to make it hold together. The laser will leave about 0.2mm of kerf, and the thickness could be either 1/8" or 1/4" (the latter is a lot more expensive). The coaster is intended to be 3.5" diameter. I would prefer not to have any kind of backing.
My first thought (if I can admit it here) is just glue around the edges, insert into the framing circle, and hope for the best. A slight refinement is that if maybe the inner pieces are clamped first (as I see done for cutting boards) and that part is glued into the frame (which I don't see how to clamp) it will hold better than the first idea.
I hope this is not too naive a question. Basically, will this work at all? If so, how would I do it? I would prefer not to have to do any drilling or cutting to the pieces.