President Vladimir Putin’s spokesman dismissed rumors the Russian leader is ill, assuring skeptics he is doing well in spite of recent appearances indicating otherwise. Kremlin diplomat Dmitry Peskov scoffed at the ongoing speculation during a sit-down interview with NBC News senior international correspondent Keir Simmons. Recent clips showed Putin, 69, “limping, shaking and gripping a table,” yet another hint to him facing serious health issues behind the scenes. Some of the theories include that he’s secretly battling possible blood, thyroid, or abdominal cancer. Other reports claim he has …