LED light muliplexing
10V at 200mA is 2W, not 20W. 

Yes, you could switch between two lamps like that, and if the circuitry is well-designed there should be no problem. 

However, five seconds is about worst-case for causing thermal fatigue in the LED strings, so you may experience early failures (months rather than years). Or not, depending on the quality of the solder and other materials that are used.