Come on people. Take a step back and see the big picture. This is not a stressful job.
If the dispatcher asks what's broken, tell them. When all the boxes are checked and everything is done we'll get an out time. If that happens to be when our scheduled out time is that's great. If not. Oh well. If you honestly believe that telling dispatch about an issue is what made you a minute late then put it in your delay report, move on, and let management hash it out in their daily meetings.
Although things have the illusion of being "time sensitive" my job is to make sure everything is completed correctly when I'm moving an airplane from point A to B. Whether or not we're on time is honestly someone else's problem.
We're airline pilots. This isn't the last flight out of Saigon. "Time sensitive" really isn't something we should be considering as part of doing our job correctly.