Here's a neat little trick you can use in Acorn 7 and later. If you have a single layer you'd like to crop without changing the size of the image (for whatever reason - I know you have one), you can use the crop tool like you normally would, and when holding down the option key when you're ready to make your crop, the "Crop Image" button in the palette will change it's text to "Crop Layer". Clicking on it will trim your layer of unnecessary pixels. You can also double click on the canvas with the option key down and Acorn will crop the current layer only.
You can of course get the same effect using the select tool, using the Select ▸ Inverse menu item, and then pressing the delete key. But our minds all work a little different so it's nice to have multiple ways of doing something.