It should be possible in most tools. I'm also using Greenshot, and this tool can be set to copy to the clipboard in jpeg as follows :

• Right-click the Greenshot traybar icon and select "Preferences..."
• In the "Output" tab set your folder and and name
• Set also the "Image format" drop-down box to "jpg"
• Set the "JPEG quality" (mine is 100%)
• In the "Destination" tab ensure that the only checked option is "Copy to clipboard"
• Click OK.

While any image is in the clipboard, it's not in JPEG format or any other disk-oriented format. It will be in a memory-resident format which is bitmap or PNG.

To get for example Greenshot to save the image on the disk as JPEG:

• Right-click the Greenshot traybar icon and select "Preferences..."
• In the "Output" tab set your folder and and name
• Set the "Image format" drop-down box to "jpg"
• Set the "JPEG quality" (mine is 100%)
• In the "Destination" tab ensure that "Save directly" is checked ("Copy to clipboard" is optional and not required). You can optionally add a check-mark next to an image-editor that will open automatically the saved image
• Click OK.

It should be possible in most tools. I'm also using Greenshot, and this tool can be set to save in jpeg as follows :

• Right-click the Greenshot traybar icon and select "Preferences..."
• In the "Output" tab set your folder and and name
• Set also the "Image format" drop-down box to "jpg"
• Set the "JPEG quality" (mine is 100%)
• Click OK.

It should be possible in most tools. I'm also using Greenshot, and this tool can be set to copy to the clipboard in jpeg as follows :

• Right-click the Greenshot traybar icon and select "Preferences..."
• In the "Output" tab set your folder and and name
• Set also the "Image format" drop-down box to "jpg"
• Set the "JPEG quality" (mine is 100%)
• In the "Destination" tab ensure that the only checked option is "Copy to clipboard"
• Click OK.