Dash has this on his website:
Explore Soviet watches: Kirovskie, Kirova, Kirov, Кировские, Watch, Часы, USSR, СССР
mroatman.wixsite.com
I haven't had a chance to look for the catalog entry, so I don't know if either of you have the right crown, but Dash is in most cases correct. Red second hand is IMHO not right. Many people took the gold ones and painted them red, it was a "thing" in its day. It looks like that's what happened to this one, so if you can strip the lacquer without damaging the gilding underneath it would be ok. Movement is correct. Personally, would skip this unless cheap and you feel like taking on a project.
The 1960 catalog confirms your thoughts that the model shown should have a gilded second hand; it also looks very nice with the red though.

It could be a second hand replaced with a red hand from a Kirovskie model. The black dial version has a red second hand.
For the model shown:
Оформление ЧН-668К
Корпус хромированный пылевлагонепроницаемый
диаметром 35 мм ; крышка из нержавеющей стали.
Стекло органическое сферической формы.
Циферблат белый с полной оцифровкой 1—12.
Цифры золотистые. В центре циферблата рисунок блед-
ножелтого цвета. Минутная шкала с шестьюдесятью де-
лениями, каждое пятое деление с оцифровкой. Шкала
и надписи на циферблате черные.
Стрелки золоченые.
Оформление ЧН-670К
Рисунок в центре циферблата окаймлен золотистым
ободком.
В остальном аналогично оформлению ЧН-668К.
Registration of ChN-668K
Housing chrome-plated dustproof
diameter 35 mm; stainless steel cover.
Glass organic spherical shape.
The dial is white with full digitization 1-12.
The numbers are golden. In the center of the dial, the pattern is pale
no-yellow color. Minute scale with sixty de-
divisions, every fifth division with digitization. Scale
and the inscriptions on the dial are black.
The arrows are gilded.
Registration of ChN-670K
The pattern in the center of the dial is framed in gold
rim.
The rest is similar to the design of the ChN-668K.
The black dialed version:
Mine:
Оформление ЧН-665К
Корпус хромированный пылевлагонепроницаемый
диаметром 35 мм ; крышка из нержавеющей стали.
Стекло органическое сферической формы.
Циферблат черный с полной оцифровкой 1—12.
Шкала с шестьюдесятью делениями. Цифры, шкала и
надписи на циферблате белые.
Часовая и минутная стрелки золоченые копьеобраз-
ные, секундная окрашена в красный цвет.
Registration of ChN-665K
Housing chrome-plated dustproof
diameter 35 mm; stainless steel cover.
Glass organic spherical shape.
The dial is black with full digitization 1-12.
Scale with sixty divisions. Numbers, scale and
the inscriptions on the dial are white.
Hour and minute hands gilded spear-shaped
seconds, the second is colored red.