No you don't. You need to have a signal going to the ECM that makes it think there is an O2 sensor in two places. There are O2 simulators that many have used on cat-less setups to simulate the second O2 sensor's signal and make the ECM think the cat(s) is/are OK.
The first O2 handles A/F ratio, the second one is just to ensure the cat is doing its job. While it would be foolish, maybe even stupid to remove the first O2, many owners running without cats have installed O2 sims to fool the ECM so the engine CEL will not illuminate. Do a Google search for O2 simulator, you'll see a number of them available from different sources.