Nice work, especially for your first re-scale.

Yes, a wedge will keep tension on the pivot and provide clearance at the tang.

Also drill your pin holes while the scales are flat, to ensure that they are perpendicular to the inside face, so you do not have issues centering the blade. It is almost impossible to drill both holes square on a non-flat surface.

If you do not glue the wedge, you will have a bit of wiggle room to adjust the wedge and center a blade, especially with wood, as wood will move with moisture variation. A properly pinned wedge will remain tight and can be trimmed tight to the scales with a file and sanding.

Here is a good video on drilling perpendicular holes on a non-flat scale.

The jig is shown in use at about 8:05 in the video.

()