All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
Vowing to shave one's head is a vow to do something permissible. In Al-Majmoo‘, An-Nawawi mentioned that, contrary to Ahmad the Shafi‘i, Maliki, Hanafi and Thahiri scholars hold the opinion that vowing to do something that is just permissible is not binding. To support their opinion, the majority of scholars quoted the Hadeeth where the Prophet, sallallaahu ‘alayhi wa sallam, said: "A vow is only binding when the person vows to do something by which he seeks to please Allaah." [Abu Dawood; Al-Albani: reliable]
Although the Hanbali scholars consider this vow binding, they do not hold that it is obligatory to fulfill it. Their views are divergent as to whether expiation is due or not in case of non-fulfillment of such a vow.
It is better not to fulfill such a vow and offer an expiation instead because the scholars consider shaving the whole head for a purpose other than Hajj or ‘Umrah disliked in the Sharee'ah. Offering an expiation like that of breaking an oath constitutes a way out of fulfillment of the vow. According to some scholars, the preponderant opinion is that the expiation is due when one does not fulfill a vow to do something permissible.
Allaah Knows best.