Should he wear gloves during tawaaf so that he will not touch women?

It is not permissible for the muhrim, man or woman, to wear gloves in ihraam, because the Prophet (peace and blessings of Allaah be upon him) said: “The woman in ihraam should not wear niqaab or gloves.” Narrated by al-Bukhaari, 1838. 

Even though this hadeeth speaks of women, the scholars are agreed that it is also haraam for a man to wear gloves when he is in ihraam. See al-Mughni, 5/120; Fath al-Baari, 4/53. 

With regard to touching women during tawaaf and saa’i, touching a non-mahram woman is haraam, so men should be careful and keep away from places where women are. If he touches a woman by accident, then there is no sin on him, because Allaah says (interpretation of the meaning): 

“And there is no sin on you concerning that in which you made a mistake, except in regard to what your hearts deliberately intend”

[al-Ahzaab 33:5]

With regard to wudoo’ being invalidated by touching a woman, this has already been answered in question no. 2178. The most correct scholarly view is that touching a woman does not invalidate wudoo’. 

Shaykh Ibn Baaz (may Allaah have mercy on him) was asked about the ruling on the tawaaf of a man who touches a non-mahram woman. He said:

If a person touches the body of a women when doing tawaaf or when it is crowded in any place, that does not affect his tawaaf or his wudoo’, according to the more correct of the two scholarly views. The scholars have disputed the question of whether touching a woman invalidates wudoo’, and there are several views. 

It was said that it does not invalidate wudoo’ at all. And it was said that it invalidates wudoo’ in all cases, or that it invalidates wudoo’ if it is accompanied with feelings of desire. 

The most correct of these views is that it does not invalidate wudoo’ at all, and that if a man touches or kisses his wife, that does not invalidate his wudoo’ according to the most correct opinion, because the Messenger (peace and blessings of Allaah be upon him) kissed one of his wives then he prayed, and he did not do wudoo’ again. And because the basic principle is that wudoo’ remains valid and one remains pure. Hence it is know that if a person’s body touches a woman’s body in tawaaf, his tawaaf is still valid. The same applies to wudoo’; if he touches his wife or kisses her, his wudoo’ is still valid so long as nothing comes out of him. But a man does not have the right to deliberately touch the body of a woman who is not his mahram. 

Majmoo’ Fataawa wa Maqaalaat Mutanawwi’ah, vol. 17, p. 218-219.