wa ʿalaikum al-salām wa raḥmatullāhi wa barakātuh
It is permissible to dye white/grey hair with any color except black, for both men and women. That is the general rule in our madhhab, however, there is an exception: a married woman may dye her white/grey hairs black if her husband does not object to it.[1]
It is recommended to use ḥinna, however, one may use commercial dyes provided that they are free from animal ingredients, impure substances such as alcohol, and harmful chemicals.
Allah knows best.
[1]Baʿishn, Bushra-l-Karīm (p710, Dār al-Minhāj)
Answered by Shaykh Omar Mohsin