The 3/16" angle will work. It just wont be as rigid. Will it affect your cutting speed? I doubt it.
The KRMx01 is a design is flexible enough that you can make many changes. The thickness of the angle is one of them. I used 1/4" be cause it was more rigid than the 3/16".
Would I use 3/16" if I were building another KRMx01 machine. one? FYI I have a set of the 1/4" 2x2 Y-beam angles on hand (with holes). If you were close to me I would give them to you.
Author of: The KRMx01 CNC Books, The KRMx02 CNC Books, The KRmc01 CNC Milling Machine Books, and Building the HANS Electric Gear Clock. All available at www.kronosrobotics.com