If you apply for and are granted a Prior Learning Assessment (PLA), you might be able to skip some or all of your training. Again, it depends heavily upon the trade and degree in question. But, for example, I have a mechanical engineering degree. While what I learned in school may have prepared me to undergo the military's training, absolutely nothing I learned in school would have resembled the training that any of the NCMs in our branch undergo.
To get the result you're looking for, honestly you pretty much have to be looking at some sort of technical or community college. PLAs seem to be all about knowing how to do hands on work. Not knowing the theory behind the hands on work.
I can perhaps think of one or two examples where a degree might involve enough hands on work to allow for a successful PLA for their NCM equivalent (Bachelor of Nursing for Med Tech Training perhaps? Maybe?) but I don't think you're going to get much luck getting out of entire courses. You might get out of aspects of a course. If they have a math course designed to bring people up to speed from the Grade 10 level, and you have a BSc in Math, then you might be able to get the occasional afternoon to go to the gym.
Of course, if you tell us which degrees you have and which trades you're thinking of, we might be able to give you a better idea.
Oh, and having relevant degrees might help for promotions at later ranks too. Again, depending upon the scoring criteria for promotion boards in that trade in that year.