deSitter:
I agree a good start - so try this - a deployable paddle, a tiny wing, whose stall angle would provide a good airspeed figure. The onset of stall would be measured by moment arm on the paddle axis.
I had a related thought a while ago, however using a small paddle that
already exists - the AOA sensor.
Seems one should be able to get a rough air speed reading by using the existing (at least in some designs) damping/test coils to deflect the AOA sensor vane up and and then down a couple of degrees.
Airspeed would be (nonlinearly,very I suspect ) proportional to the current required to achieve the target deflection. Would also need altitude etc for density.
(Do this to one at a time of course)
One nice feature of this is that at no new sensors and possibly even existing HW could be used.
I have no knowledge of where the damping coils sit in the system, I have just seen them mentioned.
If not suitable it would be possible to create a new "fit compatible" sensor with dedicated drive coils.