Assalamu Alaikum Ustadh If a woman is travelling and cannot perform wudu because she is surrounded by non- mehram men, but she can perform tayyammum, what is the ruling?

As long as she can complete her wuḍūʾ without uncovering what is awrah in front of the non maḥram men, wuḍūʾ remains obligatory and she performs it, if needed by shielding herself with a garment or a companion, using a covered place, or delaying the prayer to later within its time until she can reach privacy. She turns to tayammum only if she genuinely cannot use the water except by exposing her awrah, and in that case her prayer is valid and she does not repeat it. But if the water could in fact have been used and she left it only out of shyness, then the tayammum was not valid and she repeats that prayer, because embarrassment by itself is not an excuse.