i had exactly the same problem once, a gap of about 1/16 in.
i considered epoxying in a thin wood spacer, or plastic, or brass, or winding it with thread and resin then finishing the lumps. finally found this acrylic 'epoxy' putty that comes in colors. you knead it between your fingers to mix the two parts then push it into the gap (i used a thin wood coffee stirrer to push it all the way down to the tang & build it to the surface), wet you finger to wipe the edge smooth and flat (
best bit - it cleans up with water until it hardens) and you are done. a few hrs. later it's hard as a rock. or horn. fills insect damage in wood or horn too. no sticky overruns, no taping, no hand tools , no heavy sanding/polishing, very little mess. it just works. if you need it a bit less viscous, a couple drops of water mixed in softens it a bit more. but don't overdo it. too a few hours and it's permanent. the box colours do not correspond to the putty colour, read the labelled colour text. the red box is 'yellow grey', the blue is 'silver grey', the terracotta, white and black are those colours tho.
.
i'd try black - the white might be too white to match the ivory.