Thin hot hide glue or titebond would be what i would use. When gluing cracks like that i blob some on the surface and then mash it in with my fingers, working the crack up and down at the same time which pulls the glue down into the crack. Stick a little mirror inside and a little light bulb so that you can see the underside of the crack, and work glue in until you see glue beads coming through the length. If it needs to be clamped shut at all ( it doesn't look like it will but it is hard to tell) i would make a little wedge to fit in the F hole to wedge it closed. I would probably also clean up the glue beads on the inside and put a crossgrain cleat or two in there, you are in luck that the crack is so close to the F hole, if you are set up with hot hide glue you can just hold them in place for 30 seconds or so, if not handy magnets or a tiny clamp would work.
None of that stuff should have any noticable effect on the sound of the instrument, most of the nice old vintage instruments that everyone loves so well are peppered with cleats and patches on the inside.
_________________ Jordan Aceto Ithaca, NY
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