No, I am almost positive the only way of doing this is removing the ability, and then adding it back.
Yes and i think this question is very stupid,"Is it possible to reset ONE ability cooldown without playing into removing/adding rest of abilities? "
it is like you say is it possible to remove unit without action - remove unit
if you need it to work on a hero just set integer = level of your ability for your unit,remove and add ability,set level of added ability to integer
its solved and there is no need to find another way...
BTW there are some things that you could post (i guess)
how to get value for
gold/lumber of something (not solved on good way)
damage of some unit
armor of some unit
damage of some spell
color of unit (not so important but it would be good)
remove icons attack/stop/patrol/hold position...
patrol/hold position (not solved on good way)
there is a custom script to get gold/lumber value but i cant make it work
its something like
GetTotalGoldCost (GetUnitTypeled(GetTriggerUnit())