clock operating switch
The best and easiest solution for you would be to use regular relays,  the electromechanical kind. They are slow, but certainly fast enough for what you need. 200mA could be high for IC kind of signal-agnostic switches which are easily available. Most relays can handle that current without breaking a sweat. 

You would use a clock generator of some sort to create a signal that toggles every 15 seconds. This signal can be fed into the gate of a transistor to turn on one of two simple SPST relays or flip the direction of a SPDT/DPDT relay. In case of using two relays,  you would use a not gate (or reverse the relay coil drive cricuit) for the second relay, to make them react in opposite ways to the original signal. 

The problem you will face, though, is that 15 seconds is a long time. I'm not sure if a 555 and similar will be able to generate such low frequencies. You have two options.  One would be the expensive route of generating the 1/15 Hz square wave in the firmware of some microcontroller. The other, and cleaner solution,  would be to use the 555 at a low frequency which it does support. It should be able to go down to 10 Hz atleast, i think,  but you should check the datasheet. You can then reduce the frequency using a frequency divider circuit, which can easily be made using a binary counter (or multiple binary counters cascaded for greater dactors of division)