While not particularly sophisticated what I've done in the past is use a strip of clear plastic.
Over the years I've kept pieces of blister packs, binder sheets and various pieces that could be used as shims.
After I approximate about how much thickness I need and find an appropriate piece,I cut a strip that's maybe an inch long and the width of the bottom of the dovetail. Put it across the bottom of the dovetail and push the sight blade in. The plastic strip will move along with the blade as the blade goes in which is why the extra length.
Trim off the sides.
Not very visible.
Basically, what you are already doing with the brass shim.
