Praise be to Allah.
First of all, please see Question # 1200 for an important ruling of mixing of the sexes.
Secondly, it is not permissible for a woman to go out of her house wearing perfume. Whoever does that is exposing herself to the stern warning. It says in the hadeeth which was narrated from Ghumaym ibn Qays that, “The Messenger of Allaah (peace and blessings of Allaah be upon him) said: ‘Any woman who perfumes herself then passes by people so that they may smell her fragrance is an adulteress.’” (narrated by al-Nasaa’i, al-Zeenah, 5036; classed as hasan by al-Albaani in Saheeh Sunan al-Nasaa’i, 4737).
The Messenger of Allaah (peace and blessings of Allaah be upon him) commanded women who go to the mosque not to wear perfume; whoever does that has to wash herself. It says in the hadeeth of Abu Hurayrah that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “When a woman goes out to the mosque, let her wash herself from perfume as she washes herself from janaabah (impurity following sexual activity).” (narrated by al-Nasaa’i, al-Zeenah, 5037; classed as saheeh by al-Albaani in Saheeh Sunan al-Nasaa’i, 4738)
Thirdly: with regard to a fasting person inhaling the perfume, this does not matter. Shaykh Ibn ‘Uthaymeen was asked about that and he said: it is permissible to use it during the day in Ramadaan and to smell it, except for bukhoor (incense) which should not be inhaled, because it has a substance which may reach the stomach and it is smoke.
Fataawa Islamiyyah, 2/128
If you find traces of this woman’s perfume spray in your throat, there is no sin on you in sha Allah. The point is that the fast is broken when something that has substance reaches the throat as a result of a deliberate action. This perfume does not have any substance, and you have no sin in the matter and are not doing anything deliberately. Allaah says (interpretation of the meanings):
“And there is no sin on you concerning that in which you made a mistake, except in regard to what your hearts deliberately intend. And Allaah is Ever Oft‑Forgiving, Most Merciful” [al-Ahzaab 33:5]
“Our Lord! Punish us not if we forget or fall into error”
And Allaah knows best.