Version 1.8.0 added a new feature:
Portable Cropper. If you run cropper from a thumb drive you can add a file named cropper.portable to the application directory. If Cropper detects this file, it will save the configuration in the application directory and will default to
a sub directory named 'Cropper Captures' for the images.
So yes, Cropper can run from a usb memory stick and that is how you set it up.
Were you doing a capture using print screen or making Cropper a specific size that covered your left monitor?