Often beeswax is used to seal small air leaks on some musical instruments. One of the disadvantages of beeswax is that it has a melting point of around 140 degrees Fahrenheit and can therefore flow to other parts of instruments with deleterious effects. Do you know of a nontoxic substitute for beeswax with a higher melting point?
Beeswax is a naturally-occurring hotmelt glue, and the earliest (artificial) hotmelt glue compositions contained beeswax as one constituent. Now there are hundreds of different modern hotmelts available in which synthetic and natural waxes and resins are blended together to yield a broad range of melt temperatures and glue line strengths. I recommend you have a look at some hotmelt manufacturers' brochures & technical data; perhaps you can find a suitable beeswax replacement to test in your application.
However, note that an important quality of adhesives for musical instrument repair is the ability to undo them with heat and moisture to facilitate future repairs. The worst possible thing you can do to a clarinet, guitar, saxophone or violin is to repair it with an epoxy, cyanoacrylate or urethane glue because those will make it impossible to disassemble. So, be cautious!
You might try https://en.wikipedia.org/wiki/Polycaprolactone It softens at hot-water temperatures and is safe to handle. (You'll probably need to heat it a bit above that to get to fully liquid.) FDA approved for some applications, so IMHO pretty safe. This material is usually sold in granular form; some names I've seen are Polymorph, ThermoMorph and "friendly plastic."
But especially if this is a wooden instrument, be careful and if possible test on similar materials (to your instrument) before using it on your instrument. My concern is that it'll soak into wood and change the stiffness and thus tone.