This xdotool command will simulate holding down left mouse....
Bind this command to a keyboard shortcut or use easystroke to bind it to a spare mouse button....
xdotool mousedown 1
I describe HERE how to use easystroke.
sh -c "sleep 0.2 && xdotool mousedown 1"
Just alter to use a command instead of key.
You will need to install xdotool and easystroke.
Whichever way you set it up, once activated you just need to press left mouse to release the dragged item.
Another option would be use this script as a left mouse up/down toggle and bind to a single key like F8.
Press your shortcut key once for left mouse down....press again to release.
Use the full path to the script as the command.
# script to toggle left mouse button up/down.
# Initial run will create ~/.mouse-state.txt and will then toggle with subsequent runs.
if [ "$(cat ~/.mouse-state.txt)" = "0" ]; then
sleep 0.2 && xdotool mousedown 1 && echo 1 > ~/.mouse-state.txt
sleep 0.2 && xdotool mouseup 1 && echo 0 > ~/.mouse-state.txt