The only shipping/receiving job that I thought was more intense than lifting at a gym was UPS, and that is only if you are unloading, not loading. Unless you get a million items in one truck that are all just under the weight required to be considered "irregular" (weird shaped awkward heavy items that go in the truck last). However, if you are not in decent shape to begin with, working at UPS, FedEx, or whatever the Canadian equivalent is of those shipping companies would probably be unpleasant. Also if you live in a very hot or very cold climate, it's extra unpleasant. I am assuming the winter temperatures in those trailers would be kinda brutal where you are.
I have worked in receiving at a couple of retail businesses as well, and from my experience the boxes were too light for building muscle.
(Also, all of this was pre-transition. I had an OK squat/bench/deadlift total before transitioning and was capable of doing dips with a lot of weight strapped to me, so don't let anyone tell you just because you are pre-T that you can't lift or work a manual labor job. It is possible. I have no injuries. If anything, lack of exercise messes your joints up worse than weights or a little manual labor will.)
Anyway, good luck with your job hunt. With a decent paying job, a gym membership should be affordable. In the United States, there are gyms as cheap as $10 per month. Maybe there is something like that in Canada?