Sasuke doesn't always add Rikudu chakra to his attacks. The following manga panel confirms that:
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Above we see Sasuke saying that he would use the six paths chakra too. This means that he can choose whether or not he wants to add Rikudu chakra to his attacks. As you correctly mentioned, Kakashi's chidori was black when he used Rikudu chakra.
Similarly, with Sasuke, his Chidori is only black when he uses Rikudu's chakra. Therefore, this would imply that he slashed Madara in half with a chidori sword not containing Rikudu chakra (since it wasn't black). We also know that only senjutsu can harm perfect juubi jins. Hence, Sasuke must have used senjutsu or else he wouldn't have been able to hurt Madara.