This is an old, but painful issue with control point modeling in Rhino.
As @Tom_P mentioned above, the best workaround to slide a control point along the control polygon precisely is to use the scale (I prefer “Scale1D”). It’s super tedious and inconvenient, at least in older Rhino versions like Rhino 7 (which I use currently).
An alternative is to activate the drag strength, set it to something like 10 or lower, then change the drag mode to “Control polygon”, then select the control point you want to move along the polygon, then drag it. That greatly reduces the real risk to move the control point in a random direction, which is a huge bug in Rhino, because its “Control polygon” mode is not capable of maintaining the sliding of the control points strictly along their control polygon. Often times the direction changes for no obvious reason, especially if the Osnap is active (which literally kills the ability to snap to a reference point while sliding the control point along its control polygon).
A reminder to the developers that secondary drag strength handles are super necessary for precise control point modeling. They allow the user have an instant access to two different drag strength settings (100% plus a custom %) at any time.
Not to mention that being able to switch between the different drag modes via a single mouse click on the “Mode” handle (if using the proposed Super Gumball) makes everything much faster and more convenient than the current implementation.