Can Sons become Wali In Mother's Nikah according to the Shafi'i madhab?

AssalamAlaikum A woman(38 year old approximately) whose husband was died appropriately 7 years ago. She Has 2 adult daughter and adult 2 Sons. She is Living in her husband's home who died.She Is Not depending on Father or bother .she totally depending on self. She And Her Sons earn for their living. Now question is that if she wanna get married with a person and her sons and daughter are satisfied . Can son become wali of her Mother? She never wants to show next Nikah Due to society and relatives issues because regrettably in our society point out her this decesion in this age. Please Answer that . Can she make a secret marriage if sons become wali and two Muslims For Evidence. It will must valid and governmently registed Nikah. And Boy will also never show to his parents about this marriage. If both Are Shafi'i then please is it w Valid