Would a lower degree thermostat help to keep a Chevy 350 run cooler?

Yes, given that there aren't other issues with the cooling system. Is the fan in good shape? Is the fan shroud in good shape, or even there at all? Has the cooling system been flushed recently? If all of these things are in good working order, then yes, a 160 degree thermostat will obviously run cooler than a 195 degree thermostat will. One more question... Is the radiator big enough? That is the next question after you have eliminated possible problems with everything else.