What configuration would limit my DSLR’s shutter speed to 1/200?

Basically all digital cameras are set in a range of 1/160 to 1/250 shutter speed when flash is placed. That is calculated due to the shutter speed versus flash light bouncing back to your sensor. It comes as factory setting and there are some tricks to bend that. Because of this attribute, in any mode, the camera takes the shutter speed-when shutter speed is given below factory setting- to the safe zone.

For Canon since you asked for it there is Highspeed mode on Canon flashes where you can get up to 1/1250 safely depending to the flash model and object distance. Also without using the hotshoe and connecting the flash from side trigger, you can get up to 1/320 safely, 1/400 and 1/500 at your own risk.

Also there are some triggers and their special softwares delaying the shutter to sync with the flash for lower shutter speeds. For that I could not make any of those work properly with canon below 1/1250 shutter speed on canon mkII, mkIII, 7D, IdmkIV but on nikon d300 and d3x, I have tested up to 1/4000 without any problems.