I don't have a 1 click solution for you, but I do think that we can find a way.
Just adding the volumes to the robot is quite easy. You just have to create geometric shapes on top of the robot model. Exactly like you did. The only thing you need to do is making sure the origin of these shapes is at the base of the robot.
To keep the same kinematic, you can simply modify the existing robot by entering debug mode. "Ctrl" + "Alt" + "Shift" + "G" (latest version of RoboDK)
Right-click the robot and "Modify Robot".
Convert the copy of the robot to object - Select all "little cylinders" -> Right-click -> "Convert to Object"
Merge the existing 3D models of the robot Joints and the Shapes you created: Select both parts -> Right-Click -> "Merge"
You then replace the 3D model in the "Modify Robot" window. Make sure to select the right reference frame, otherwise, the parts will fly around.
Now, we have a robot with a safety zone.
Using this robot all the time is not perfect. But the way it's created, we can't just hide the safety zone.
But what we can do is use a normal robot for our simulation. When it's time to do the collision checking, you "unhide" the safety robot and "hide" the normal robot.
At this point, if you run the program you created, nothing will happen because the program will run on the hidden robot.
But if the safety robot is set to mirror the joints of the normal robot, both robots will follow the exact same paths.
There's a script Albert wrote not so long ago the does exactly that. Here's the thread: https://robodk.com/forum/Thread-Select-m...ght=mirror
I hope it helps.
Let me know if you need more info.
I might edit for clarity tomorrow.