This is not the done in European ports. You might find some taxi drivers in some who are willing to drive you around, but they are not guides and may have very limited English. Besides, cost could be a problem since you would have to agree to some price set by the driver. It is much better to book with a tour company.
In Santorini, there are no taxis at all for casual tourists. The only taxis are at the ferry port where only ship tours are tendered to. So, you could not get to those taxis because you cannot get to that port without a ship's tour. There is no road to the cable car port, only the cable car, donkeys and your feet. As previously said, from that port you can get a boat to take you to Oia or maybe a boat tour to take you to the volcano islands in the caldera.