Fairly easy to do with a stanley 45....Knife both sides of the dado, as to do 1/8" x 1/8" deep dados you will be using just the main body....and a batten to guide the plane along....should only take ..3-4 passes, move to the next dado..The reason for the knife wall ( as Sellers calls it) is you are going across the grain...and can't very well use the 45's spurs. Yes, Stanley did make a cutter that narrow, BTW...
I seem to remember that cubby/pigeon holes that used thin dividers...simply slid the dividers in "V" shaped grooves....the dividers had their ends beveled to match...might be a bit easier to do than a regular square walled dado?