Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother in Islam, thanks a lot for your question which shows your keenness on abiding by Allah’s laws and teachings. May Allah enlighten our hearts with the light of Islam!
Sa`i is the devotional act of walking seven times back and forth between the two hills of As-Safa and Al-Marwah. This act retraces the footsteps of Hajar (wife of Prophet Ibrahim), during her desperate search for water for her infant son Isma`il after they were left in the desert by Prophet Ibrahim in response to a divine vision.
With regard to your question, the late Sheikh Ibn `Uthaymeen, a prominent Saudi Muslim scholar, (may Allah shower mercy on his soul), issued the following fatwa:
It is not permissible to perform a voluntary Sa`i, because Sa`i is only prescribed as part of the rituals of Hajj and `Umrah. Allah says: (Surely Safa and Marwa are among the signs appointed by Allah; so whoever makes pilgrimage to the House or pays a visit (to it), there is no blame on him if he goes round them both; and whoever does good spontaneously, then surely Allah is Grateful, Knowing.) (Al-Baqarah 2:158)
Allah Almighty knows best.