TL;DR Tape over it.
Disregarding whether that's a good idea or not*, the easiest way to 'disable' the LED is most likely to open up your laptop case and unplug the LED ribbon cable. Barring that as a possibility, the next most practical solution would be place tape (or an aesthetically pleasing sticker) over the LED.
While it may be theoretically possible to modify chip firmware somewhere on your motherboard to disable the LED, there won't be any easy way to do so in a software setting expressly because the engineers designing computers, for various reasons* believe that to be a bad idea.
*See e.g. this user's comments on (now archived) notebookreview.com forums; relevant quote:
The light serves one major purpose. Telling you when the HDD is being
read or written too. That can allow you to quickly determine whether a
"hang/lockup" is really a lockup and not just a temp. slowdown due to
heavy HDD access.