The knife is excellent, this piece would have fallen off if it had not been held by the tube at the back. I had AG Russell's knife, a small ivory droppoint, it had a similar crack, sorry the photo didn't survive, the piece behind the crack fell off. Possibly due to a change in moisture?

Compressed air may or may not help, the dirt can definitely be cleaned out with pressurized water, such as Karcher, but it is necessary to wrap all the other parts of the handle with something like electrical tape stronger so as not to damage the handle. And then use in crack a little epoxy resin for jewelry, it is durable and almost invisible, but it is better to pre-experiment on some separate piece of a broken bone to see how it will look.