Is there such a thing as a Schottky zener?
A Schottky Zener does not exist*.
Back to back Zener and Schottky diode as you suggest, is a suitable method of minimising undershoot. 

A Zener is both slow and "soft". Under high energy conditions where a substantial current will flow the zener voltage may substantially exceed its rated value. If required, faster clamping may be achieved by eg using a diode to a supply rail at the desire clamp voltage. This is the direct equivalent of the reversed Schottky to ground in your example.

A reverse biased Schottky diode is sometimes mounted across a MOSFET's gate-source pins in power driver applications, with minimum lead lengths between MOSFET and diode. The reason for this is not always obvious from inspection. 
Miller capacitance effects can couple load transients into a MOSFET's gate and promote oscilliatory "ringing" which can lead to rapid switching and device destruction. The reverse Schottky clips negative oscillation peaks to a level far below the threshold voltage of almost all FETs and prevents oscillation.  

I invariably use a low wattage gate clamp zener on MOSFET gates in power applications. I seldom use a reverse Schottky. In a commercial product  with a typical MOSFET survival time of a few minutes without a zener (due to Miller coupling from an inductive load), a zener provided complete long term reliability. 



Note that when clamping to a power supply 'rail' you need to be sure that the delivered energy does not "pump the rail voltage up" by more than is acceptable. This is seldom going to happen as the energy per clamping event x events per second = clamping power will usually be lower than the load on a typical rail.

The same applies to clamping diodes used to limit the range of voltage swing on an input line so that it is (almost) within supply rails by using diode from input to positive rail and ground. If the input energy that can flow exceeds the energy being taken from the rail the rail voltage may rise. This actually happens in some real world cases. I have seen an  application note published by a major microcontroller manufacturer that used input diodes for "protection" of an input (test probe) to which AC mains could be applied. In such a case the energy flow would have been in excess of the 5V rail load and the supply would have risen to unknown higher voltage.




Note: * "Does not exist" is a strong claim. The two technologies are fundamentally different. I've never seen one but a hybrid design could be built and may exist, but simply using two components is so easy that there would not be vast demand for what would be a relatively specialised part.