Your premise with interstellar hydrogen causing decrease in oxygen in atmosphere is NOT plausible.
TL;DR: Forget interstellar hydrogen. There is plenty of hydrogen in solar system. For bonus oxygen elimination, you can burn some iron and sulfur, it is plentiful too. Anything which oxidizes would do. But you need to burn huge amounts of material, and the arrival of that material to atmosphere will be most likely visible.
Because of solar wind, no interstellar hydrogen will be able to reach the Earth orbit (even if there might be a cloud of hydrogen in interstellar space).
BTW interstellar space is extremely empty, see density of interstellar medium. "Dense" is 10^6 molecules in m3. Atmosphere on sea level is 10^19 molecules per m3. Good man-made vacuum is 10^10.
Voyager only now, after decades of flight, left outer area of solar wind influence and is really out in interstellar space.
Earth is safely tucked in heliosphere, no interstellar gas can reach us that easy.
As TimB calculated, you need a lot of hydrogen. To get such amount of hydrogen to planet so quickly, no obvious natural process is plausible. Geological changes work on geological timeline (millennia).
If you are in such a hurry, use aliens. They may hurdle small (hard to detect) balls of frozen hydrogen to planet's orbit, to eliminate oxygen which is poisonous to them. They are alien-forming this planet to their liking. Kuiper belt might have enough hydrogen-based materials for that. Build a factory on Sedna, extract hydrogen, ping it down the Sun's gravity wall toward Earth. Fun has been had by everyone involved.
Kuiper belt might have mass up to 10% of mass of Earth, most of it being hydrogen. Then there is more nearby hydrogen in Oort cloud - more than in any random interstellar hydrogen cloud, even if much farther and even more dispersed.
If you go this way (aliens alien-forming Earth), Jupiter's moons Europa, Ganymede and Callisto have lots of water too, and are closer to Earth. Io has lots of tasty sulfur which aliens prefer over the oxygen :-) But then they might just like Venus as it is now.
Of course hydrogen balls from moons would have to escape Jupiter's gravity, but because they are on the Jupiter's orbit it should not be too hard.
You would also have to slow down photosynthesis (which converts water back to oxygen). One way would be to put lots of sulfur to atmosphere (as I mentioned from Jupiter's moon IO), to start runaway greenhouse effect like on planet Venus, with high temperatures and dense clouds (preventing light reaching lower atmosphere) acid rains.
Another way to bind a lot of oxygen is iron. Iron is pretty common too. Small iron meteorites. You want them small, so they will burn in the atmosphere and do not fall down to the surface. Thousands of tonnes per day. This will be more obvious - planet's surface will be covered by red dust (rust).
Iron, hydrogen and sulfur bombardment will make beautiful night view: lots of falling stars. To avoid this (make it more sneaky), you can create iron and sulfur dust, mixed in frozen hydrogen for delivery.