If the alcohol content of cologne is at such a level that one could become intoxicated by drinking a lot of it, it is haraam to keep it, whether a little of itor a lot, and it must be poured away and destroyed because it is khamr (an intoxicant). It was proven that the Prophet (peace and blessings of Allaah be upon him) commanded the Muslims to pour away whatever wine they had when the following verse was revealed (interpretation of the meaning):
“O you who believe! Intoxicants (all kinds of alcoholic drinks), and gambling, and Al‑Ansaab,[stone altars for sacrifice to idols, jinn, etc] and Al‑Azlaam (arrows for seeking luck or decision) are an abomination of Shaytaan’s (Satan’s) handiwork. So avoid (strictly all) that (abomination) in order that you may be successful.
91. Shaytaan (Satan) wants only to excite enmity and hatred between you with intoxicants (alcoholic drinks) and gambling, and hinder you from the remembrance of Allaah and from As‑Salaah (the prayer). So, will you not then abstain?”
And it was proven that the Prophet (peace and blessings of Allaah be upon him) said: “Whatever intoxicates in large amounts, a little of it is haraam.” Narrated by al-Tirmidhi, 1865; Abu Dawood, 3681; classed as saheeh by al-Albaani in Saheeh Abi Dawood.
Based on this, it is haraam to drink it, perfume oneself with it or purify oneself with it. But if the alcohol content is not at such a level that drinking a lot of it would cause intoxication, then it is permissible to buy it and keep it and use it as a perfume or for purifying oneself, because the basic principle is that things are permissible unless there is proof to the contrary.