Change the duration for the screenshot thumbnails
The default behavior is to display a thumbnail of the image for a short delay before writing the image to the Documents folder. An alternative would be to set the Clipboard as the Save to in the Screenshot options. In this case, the image is placed in the clipboard instead of being written to a file. You can then paste the image. Here, no thumbnail is displayed, but the image in the clipboard can be viewed in the Finder. (From the Finder menu bar, select Edit➝Show Clipboard). If you need to drag and drop the image, then one method would be to set Preview as the Save to in the Screenshot options. From the Preview application menu bar, select View➝Thumbnails or the option+⌘+2 key combination. You can drag and drop the thumbnail. 

I realize your question was to increase the delay. This answer attempts to point out alternatives to having the image end up being saved to the Documents folder by default after the delay has expired.