There is nothing wrong with using alcohol-based perfumes on the body and on clothes, and that does not affect the validity of the prayer. The scholars differed as to the nature of the impurity (najaasah) of alcohol: is it physical or metaphorical? 

Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said when he was asked about the impurity of alcohol and cologne: 

The basic principle is that things are pure (taahir) unless there is evidence to indicate that they are impure (najis). When there is no evidence to indicate that something is impure, then the basic principle is that it is pure. But it is evil (khabeeth) in a practical and metaphorical sense. However, the fact that a thing is forbidden does not necessarily mean that it is impure. Do you not see that poison is haraam but it is not najis (impure)? Everything that is najis is haraam, but nor everything that is haraam is najis. 

Based on that, we say concerning cologne and similar things: they are not najis, because alcohol in and of itself is not najis. There is evidence for the opinion that we have mentioned, so cologne and similar things are not najis either, and as they are not najis, the clothing does not have to be purified from them. End quote. 

Majmoo‘ Fataawa al-Shaykh al-‘Uthaymeen, 11/252 

Shaykh Muhammad ibn ‘Uthaymeen was also asked: 

If it is proven that a perfume contains alcohol, can a person put it on his clothing and go out to pray? 

He answered: 

It should be noted that pure alcohol is not najis and it does not have to be washed from the clothing or the body. Once you understand that, you will know that perfumes that contain alcohol, even if the ratio is high, are not najis. End quote. 

Liqa’ al-Baab al-Maftooh, 176, question no. 4 

See also the answer to question no. 59899 

And Allah knows best.