You have two options:
1. don't take a region capture -- just take a whole-monitor screenshot, which doesn't involve any freezing of the image, and then select and crop the region from within the screenshot captor interface itself.
2. use red-box capture more to perform region captures -- this alternative method does not freeze the screen at all. Go to the "Selection Caption Options" and under "When to Use Red Box" choose "Objects AND Regions"