The speaker icon in the Driver list allows the driver to be muted.
When the driver is enabled (unmuted) it will affect the property as normal. When it is disabled (muted) it will no longer execute.
When muted it is possible to adjust the driven value manually. Keying into the driven field will override the scripted expression of the driver (eg, entering '0.45' will change the Scripted Expression to 0.45) - losing the old driver expression. However, in the case of shape keys you can drag left and right on the Value property to adjust its value and, providing the driver is 'muted', the new value will take effect.
An alternative option is to use keyframes to adjust the value - since if the driver is muted the property will revert to the value of the f-curve. Note, however, that the f-curve value will only be re-applied on change of frame or if you adjust the f-curve directly.
To achieve this, simply move the mouse over the Value and press I to insert the keyframe; the colour of the property should change to yellow to indicate the keyframe.
You can now adjust the keyed value via the Graph Editor window. Select the Value channel (it should be represented by a horizontal line since it's a constant), press G to Grab, and move it up and down to adjust the value. With the driver enabled the change in the graph editor should not affect the shape key. With the driver disabled, the graph editor value should affect the shape key.