What model temp controller you have? The Johnson that most brewers use, you just plug the fridge into the controller, and it cuts power to the unit once the temp hits your set point. If you are worried about the older compressor cycling too much, just make sure you set like a 3-5 degree differential, meaning if you are at a set point of 60F, and the differential is 3, the controller isn't going to supply power until the fridge temp rises to 63, then cut power again at 60. As long as your fridge is decently insulated, it's going to take a pretty long time to lose 3 degrees. It's when the differential is 1 that the fridge kicks on pretty regularly. I have my differential at 1 on a modern display cooler, and my cooler still only kicks on about every 20-25 minutes.
Hope that all makes sense! There's really no particular reason using the controller would tax the older fridge compressor any more than a newer one unless it is just popping on and off too often, which would be a insulation problem more than a function of the old compressor.