Shooting in 4:3 Aspect Ratio
Use the frame guides built into whichever camera you use, and set the guides to 4:3.  Both cameras you mention have them.  When you're shooting, compose your image inside the frame guide.  The camera will record outside of that area, but when you edit, you'll crop the image back down to 4:3.  The extra pixels around the edges allow you to do things like; recompose if necessary, correct your horizon, add or remove lens distortion, add or remove camera shake, etc.

I haven't used the A7 enough to remember where the frame guides are in the menu structure (Sony menus are famously awful.  I still have nightmares about switching to/from HFR RAW on the FS700.), but on the BMPCC4K it's dead simple, just tap the reticle icon on the top left corner of the screen, and select 4:3 from the menu that appears, and flip the toggle on the bottom left to "ON".