When I first saw the reference art, I got the feel that it was supposed to be more like an obi. Still, having no way to tie it, like a traditional obi, a waist cincher would be the way to go. An underbust corset has a different shape, and goes back up at the sides, whereas a cincher does not.
As far as whether or not to use boning, that is up to you. If you want to get the "stiff but less structured" look of an obi, you could simply use a heavier fabric and interfacing, and not have to use boning. If you choose to use boning, but do not want the channels to show, then make the channels in the lining side. However, you will have to use a heavier fabric on the outside or you will still see the lines from the boning. Personally, I think making a waist cincher using a stiff interfacing would suit this really well.
Since there is no break in the front or the back, your best option is side closure. Lacing does not work well for that and would be somewhat out of place on this particular outfit. Velcro would work, but could come apart under the strain of repeated movement. I would suggest either an hook&eye closure or a zipper. If you want it to be more snug and form fitting, a zipper would be the way to go, because the hook&eye would be difficult to close.