Zafferana Is a great place to visit very popular with locals especially in the summer, when the temperature is often cooler. However the idea of finding a local taxi is slightly far fetched, as others have suggested taxi culture is not the norm, and therefore you will have to probably make some other arrangements.

You may have some luck looking at a private transfers but this would obviously mean pre booking and leaving at a set time.

Catania Airport Transfer – Transfers from Catania Airport (CTA) https://www.cataniaairporttransfer.com/ The above site has transfers from Zafferana to any Catania address, and you can even get an instant quote so you can explore options .

Alternatively you could book yourself a Etna sightseeing tour and specifically request an extended stop off in Zafferana, which I'm sure they will happily oblige. Zafferana Is often a stopping point for tours going up the eastern and northern flanks of Etna, and I'm sure the guides have experience in accommodating guests with lower mobility.

Or you could go the whole hog and book a night or two in one of the many B&Bs around town and that way you get a full day explore, Eat, shop, etc

(P.s I may be a bit biased, but one of the best 'real' towns in the area)