If the power supply is designed properly it shouldn't be able to harm anything, it just won't work. the .2A max on the new unit compared to the .6A on the old one is a bit alarming though. The problem may stem from the newer power supply being meant for a newer model of the TV that didn't have such a high current requirements on the 15V side, or that the original power supply was over engineered. In the former case if the power supply will go into over current shutdown, in the later everything will work fine. The power supply should be fine either way, one way it works, the other it doesn't.
Personally I'd try it, but I'm not the one with property and a purchased power supply on the line so it's all up to you.