All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The basic principle is that it is permissible for men to use oils and the like, and this does not fall under the category of the prohibited imitation of women as long as the applied substance is not exclusively used by women – like women’s makeup for example. What constitutes prohibited imitation of women is when a man wears clothes that are peculiar to women or imitates them in their gestures or the like.
Al-Haytami said in Az-Zawaajir: "Grave sin no. 107: men imitating women in what is peculiar to women according to prevalent customs with regard to their clothes, manner of speaking, gestures or the like; and vice versa (women imitating men in the same sense). Ibn ʻAbbaas said: 'The Messenger of Allah, sallallaahu ʻalayhi wa sallam, cursed women who imitate men and men who imitate women.' [Al-Bukhaari]" [End of quote]
It is true that a man may be instructed and advised to avoid exaggeration in pampering and beautifying himself because exaggeration in this regard is a womanly attitude. However, this does not mean that it is forbidden for men to apply oils at all.
In principle, it is permissible for men to apply ritually pure creams that do not incur harm. As for whitening the skin, it is permissible to apply natural oils as well as the creams that do not result in permanent or long-term change in the skin color for this purpose.
As for whitening the skin using injections or bleaching pills, it is impermissible, unless it is done to correct a flaw or disfigurement.
Allah Knows best.