Every committed Muslim woman should avoid anything that might trigger temptation. In public, there is no need for the Muslim woman to wear perfumes whether light or strong ones in order to remove the smell of sweat as such smell can be removed by bathing or washing the places in which sweat is usually found.
It is reported that the Prophet (peace and blessings be upon him) said, “If a woman wears a perfume and then passes by people who smelled her perfume, she is then considered an adulteress. And every eye is liable to commit adultery.” (This hadith was reported by An-Nasa’i, Ibn Khuzaymah, and Ibn Hibban in their compilations of authentic hadiths. It was also reported by Al-Hakim who regarded it as authentic.)
The same hadith was reported by Abu Dawud and At-Tirmidhi with the following wording: “Every eye is liable to commit adultery; and the woman who wears perfume and then passes by a gathering is such and such.” (i.e., she is an adulteress).(At-Tirmidhi regarded the same hadith as an authentic hadith. We learn from reported traditions that the best perfume for women is that whose color is apparent and scent is hidden.)
From the above hadiths, describing such a woman as an adulteress means that she is like an adulteress because she wears perfume with the intention of tempting men, which is undoubtedly an abominable behavior. Temptation and seduction are not accomplished unless the used perfume is strong. However, if the perfume is light, so its smell does not spread, and if it is not used with the intention of seduction but rather for removing the smell of sweat, for example, the woman in such case is not like an adulteress because she is not intending seduction.
Nevertheless, I believe that it is disliked at least, for even if the smell of the perfume is light, there is still a risk that men will smell it due to the congestion in streets, markets, and means of transport. Thus, it is more appropriate for the righteous woman to avoid anything that might trigger temptation.
Furthermore, the smell of sweat can be removed by bathing or washing the places in which sweat is usually found [and by wearing deodorant]. It does not need wearing any perfume, because wearing light perfumes might lead to wearing strong ones.
Such prohibition is applicable only in the presence of non-mahram men, whether inside or outside a woman’s house. However, in the presence of mahram men, her husband, or other women, there is no restriction on wearing perfume, due to the absence of temptation in the presence of mahram men, or to please the husband or to avoid being criticized by other women.