Almost all weapons, shields, bows and so forth can be repaired using the method above, including those which have been fused. However, there are a few exceptions, namely weapons obtained via amiibo and magic rods. It should also be noted that decayed weapons can be fixed but they will remain in their decayed state.
There is a rumoured fix for amiibo weapons here that involves dropping the weapon and then fusing it to another weapon before giving it to the Octorok, but we haven't tried this method yet so can't confirm anything on that front.
We should, of course, also give a shout-out to Austin John Plays over on Youtube who seems to have been the first to discover this mechanic in the game!