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.
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.
Baʿishn, Bushra-l-Karīm (p710, Dār al-Minhāj)
Answered by Shaykh Omar Mohsin