It would be saturation you would want to dial down on the monitor in order get an idea of how the image will look in black and white. Remember that you will have some more control in post because you can tweak the levels of individual colors so that they read as different grey values when you desaturate. Also remember that production design is very important when shooting black and white. The colors of your sets, costumes, props, etc will play a large part in determining the contrast of the black and white image, i.e. a certain shade of blue next to a certain shade of red has good separation in color, but may read as the same grey in B&W. I think there are a lot of threads on here about shooting color to be converted to B&W.
Can I assume from the information you've given that there is no power in the cabin whatsoever? If so, LEDs are probably going to be your only viable option for battery power. 1x1 LitePanels with the v-mount or Anton Bauer battery adapter, or Roscoe LightPads seem to be the production standard in my experience. There are some really bad LED products out there, in terms of quality of construction and quality of light, though color is less important in your case so you may be able to go with some cheaper models. Before you purchase any gear, at least get a quote from a rental house. If you're only shooting for a few days you will likely have access to better gear for less money, unless you were planning to make the investment of purchasing gear anyways.
The other option that comes to mind is using reflector boards or 8x8 frames with bounce material outside the cabin in order to redirect some of the natural sunlight in through the windows. The downside is that you will have to keep adjusting the angle of the reflectors throughout the day as the sun moved, and you may lose the sun completely, or never have it at all. You can still get a decent amount of bounce on an overcast day with the hard side of a reflector board or a lamé rag on a frame.