I have extended a number of canes. I add the extension below the handle. If you oak cane is a regular hook handle you could cut the cane at a point across from the bottom of the Hook. Then drill a 5/16th hole about 3 inches deep in the shaft and in the bottom of the handle where you made the cut. If you are adding 4 inches, Cut the wood of your choice in a 4 inch piece. It can be a dowel the same diameter as the cane or a block that you can shape. Drill a 5/16th hole though center. Then using a 10" 5/16th all-thread epoxy them together. I do not have a picture but the last one I did was a 1 " diameter walnut cane. I added 2 3/4 " to it. I cut two 1" squares out 3/4" blood wood and one 1" square out of 3/4 ash. I had the walnut shaft, then 1 blood wood the ash then blood wood, then the walnut handle. Sanded the squares to mach the shape of the cane. When finish it looked real nice. I have not done it but have seen deer antler use as a insert also. Hope that is of help.