The square module would affect the cutter's aerodynamics and might change the structural requirements for the module.

At subsonic speeds, the cutter simply has so much power, and effectively infinite fuel, that it doesn't care about the additional drag. (The flat face of the module hitting the airflow is bad; the extreme turbulent flow is worse.) This continues in the transonic and low supersonic regimes, although the dynamic pressure on the exposed corners of the module will build rapidly. If it was a shipping container, this would start to be a problem. Assuming that the cutter has advanced fly-by-wire controls with artificial dynamic stability, the buffetting caused by the exposed corners should be controllable.

As the cutter's Mach number increases, dynamic pressure on the corners also increases. Still, the cutter has so much power that it can simply push through this. At some point, you're going to be concerned about the longitudinal crush resistance of the module (pushing on the front to crush it toward the back). The cutter as a whole is very strong, but I would design normal modules with the assumption that the front and rear faces wouldn't be exposed to high dynamic pressure. At worst, this means some additional mass and volume devoted to structure, but it should be taken into account.

I'd want to have fairings added to the cutter to cover all eight corners of the module (front and rear). This would be a huge help with buffetting, if nothing else. Of course, the fairings have to be strong enough to take the pressure on them, not tear off in a high negative-G maneuver (from the perspective of the fairing), etc. Yes, at TL-12 this is all pretty trivial, I'm sure. There are real-world missiles that go to a square cross-section in the mid-body, although their cross-sections have rounded corners.

If you don't add the fairings, things get really fun when you enter the hypersonic regime. The blunt nose of a cutter is actually a decent shape for ballistic reentry (or faster). (See https://www.airspacemag.com/space/how-the-spaceship-got-its-shape-137293282/ ) The cutter nose is not so good for subsonic, transonic, or even supersonic drag, but, again, it has enough power that it gets to not care a lot of the time. When exposed corners are hypersonic, they become hot spots where the atmosphere gets compressed and super-heated. Make sure that you have good thermal properties, insulation, cooling, materials that aren't weakened by extreme heat, etc., etc. because the front of the module is well ahead of the cutter's center of mass, any deviation from a zero angle of attack (pointing straight into the airflow) will cause a powerful dynamic instability reinforcing the movement. In other words, if you yaw a bit to the right, the left corners will "catch" the hypersonic flow directly. Be sure that you have extremely strong controls, preferably thruster plates capable of 15G lateral thrust, or extendable control surfaces at the tail.