Single word for delaying an unpleasant task
Solution 1:
The verb procrastinate / noun procrastination is an almost exact fit:
procrastinate verb [ I ]
to keep delaying something that must be done, often because it is unpleasant or boring
[Cambridge English Dictionary]
Note that this means 'delay/ing an unpleasant task'; it takes no object (the 'unpleasant task' is implied).
Solution 2:
Your instincts about "dragging" are correct; however, the term in actual use is
foot-dragging
Oxford:
Reluctance or deliberate delay concerning a decision or action.
Merriam-Webster:
failure to act with the necessary promptness or vigor
There is an implication here that the person dragging their feet is under some obligation to do something or go somewhere, but is unwilling to do it. You can drag your feet even in taking an action to start your task.
Solution 3:
to temporize TFD
- To act or speak in order to gain time, avoid an argument, or postpone a decision
As in:
Facing an unpopular task, he temporized, hoping it would "go away".