Check out this Wiki article on bicycle wheel sizing:
https://en.wikipedia.org/wiki/Bicycle_wheel#700C_road_bicycle_wheels_/_ISO_622_mm
700C and 29"ers use the same rim diameter - 622 mm. Typically you can go from a smaller nominal tube size to a larger nominal tire size, but not vice versa. E.g. Your 35 mm tire is about 1-3/8". You could use a smaller (for example, 1-1/4", tube in a 35 mm tire), but I would not use a 2" tube in a 35 mm tire.)
I'm not sure about 27" - it seems that the nominal sizes (700 mm, 26", and 29") pertain to the approximate O.D. of the wheel and tire assembly when a typical tire is fit to the rim. It seems to me that a 27" rim/tire combination is part of the 622 mm rim family, running a fairly skinny tire.
Examples:
A 26" mountain bike tire is typically around 2" in cross-section. A 26" rim is 559 mm (22") in diameter. 22" + 2(2") = 26". But if you went with a 1.5" tire, the O.D. would drop to 25". If you went with a 2.375" tire, the O.D. would be 26.75". So, the nominal 26" is an approximation.
A 29" mountain bike tire is typically around 2.2" in cross-section. A 29" rim is 622 mm (close to 24.5") in diameter. 24.5" + 2(2.2") = 28.9". If you ran a 1.5" tire instead, you'd be down around 27.5" O.D. If you went with a 2.7" tire, you'd be up at 29.9". So again, 29" is an approximation.
So in every case, the nominal wheel/tire combination's O.D. will vary in real life depending on tire size.
A "700 mm wheel" (the nominal size of a 622 mm wheel with a 39 mm tire installed) will be more or less depending on which tire is installed. 622 mm (actual rim diameter) + 2(35 mm) = 692 mm = 27.2". I would be that's what you've got.
For what it's worth, the Schwalbe Marathon tires on my Kona Dew Deluxe say "622 x 32/28" x 1-1/4"/700C x 32". I'd think that you'd be fine with any Schrader-valve equipped tube identified for use with 622 mm/700C/28" wheels for a nominal tire size of no less than 32 mm/1.25".
Bike experts, please jump in! I may have this wrong.