This page offers a candidate for first story to propose the idea of nanotech: "A Menace in Miniature" (1937) by Raymond Z. Gallun. According to the description, the characters in the story seem to be suffering from some sort of tiny projectiles that have gotten into their wounds, and one proposes to use a robot called a "scarab" which is about a quarter-inch-long. When another character, Dr. Kurt Rolf, suggests that the robot is probably too big to be of use, the first character replies:
"...you haven't got all of my idea yet, Doc. I don't mean that you should construct this ultra-microrobot with your own fingers, of course - at least, not directly. I mean that you should manipulate the robot control, making our Scarab do the work.
Rolf was silent for a moment. Then fierce eagerness seized him...
"With the Scarab as big as a beetle, I could make a Scarab as big as a sand grain. This second Scarab could build a miniature of itself, as big as a dust grain. The third Scarab could construct a fourth, bearing the same proportions as the first to the second, or the second to the third. And so on, down, to the limit imposed by the ultimate indivisibility of the atoms themselves."
The story you mention, Microhands, was earlier though, so it depends as you say on whether Microhands mentioned the idea of building all the way down to the molecular scale. I tried running the online version in Russian through google translate and it looks to me as if the character only built the machines down to around the level of microorganisms like rotifers, though.
Also, without knowing more about "A Menace in Miniature", I don't know if the characters actually end up building any robots down to "the limit imposed by the ultimate indivisibility of the atoms themselves", but this might at least be the first story to explicitly discuss the idea.
As a side note, this article discusses the evidence that Feynman's speech on the idea of nanotechnology may have been indirectly inspired by Robert Heinlein's "Waldo" (1942), another story which featured a variant of the "remotely-controlled robots building smaller remotely-controlled robots" idea. It seems that Feynman's friend Al Hibbs had read Heinlein's story and been inspired to write up a patent based on the idea of remotely controlled robot manipulators, and Ed Regis' book Nano quoted Hibbs recalling a discussion with Feynman about it, including the idea of tiny ones:
"It was in this period, December 1958 to January 1959, that I talked it over with Feynman. Our conversations went beyond my 'remote manipulator' into the notion of making things smaller … I suggested a miniature surgeon robot…. He was delighted with the notion."