I have visited all three islands, at various occasions.
Considering that you plan to go in late winter or early spring (therefore not beach weather, or nature weather in general), and considering that you do not plan to rent a car, I would say that Sicily is the only viable option.
Neither Sardinia nor Corsica have the wealth of things to see outside of nature (wonderful beaches and mountains and countryside), compared to Sicily.
If you were going in late spring or summer it would be a totally different story.
Also both Sardinia and Corsica are difficult to visit using public transportation only. Sicily, although it doesn’t have the efficient train system as the mainland, has plenty of public transportation options, being the 5th mosto populous Region in Italy with two major metropolitan areas.