Is it sinful to recite the Qur’an without having performed Taharah (ritual purification), if there is no water or clean dust?
If situation is as you mentioned, it is permissible to recite the Qur’an without Taharah, under the general principle contained in Allah’s saying:
So keep your duty to Allâh and fear Him as much as you can
Allah (Exalted be He) also says:
...and He has not laid upon you in religion any hardship
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.