Dulcimer String Anchor Pins
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You could easily hammer in 3 or 4 metal brads or brass-plated escutcheon pins between the slot and the present wooden peg. You could just leave the wooden peg where it is. Put masking tape on that area of the wood, draw a straight line and measure for the pin locations. Then tap dents in at those 3 or 4 points, pull off the tape and carefully hammer them down to about 1/16" of the surface. If you have a tiny drill bit, you can pre-drill the holes to keep the wood from possible splits.