steel washers are sold by size. The size is the internal diameter x the
external diameter. The sizes are common, like 1/2 x 1/4. 1x3/8", etc.
Therefore, there aren't that many really. There are diff. types, and a few
thicknesses, heavy duty thickness,etc. Its often not hard to match the ID
to thedrill you are using. You could clamp a washer(s) to the end of the
dowel and use it as a guide bushing, or buy a guide bushing, or cut a pipe
of tube/pipe to do same. You could go from both ends. Then wriggle through
with a long bit, maybe auger.