I'd fill it with wood glue if it's just a tiny crack, and then after that wood glue dries you need to oil it or seal it in some way from taking on or letting out moisture. If the crack is large, you can make a paste with wood glue and fine sawdust. Remember to keep it pretty liquid or at least fill it with liquid first, so it starts to absorb into the surface a bit to create a bond, then fill it with the paste. In past years folks would commonly reccomend using super glue to fill small cracks but super glue is engineered to break down as it was created first for surgical use and needs to disappear just like some kinds of stitches. Since the only glue you're intending to leave is the stuff that's actually gonna fill the crack you can easily wipe off the excess and keep the exterior looking straight stock. For interior oil, there are plenty of blends you could use. Hopefully a bunch of people will speak up with their favorite mixtures just so we can see what's popular out there. If you feel like you can't source good oils I can send you a jar with a mixture of citrus, tung, and linseed.
The water idea would work as long as you could continue to keep it wet at all times, as in dunk it or sluice it a few times per day every day and then kiss it goodbye when you can't keep up with for a few days.