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.
The majority of the scholars are of the opinion that it is disliked for one who intends to offer an Udh-hiyah to cut anything from his hair or trim his nails during the first ten days of Thul-Hijjah. In Al-Majmoo‘, An-Nawawi said:
Shaafi‘i scholars are of the opinion that it is disliked for the one who wants to offer an Udh-hiyah to remove anything of his hair or nails during the first ten days of Thul-Hijjah until he slaughters. Malik and Abu Haneefah are of the opinion that it is not disliked. Sa‘eed ibn Al-Musayyib, Rabee‘ah, Ahmad, Is-haq and Dawood are of the opinion that it is forbidden. According to another opinion of Malik, it is disliked.
In any case, whoever deliberately or forgetfully does this is not liable for anything, and his Udh-hiyah is valid and acceptable. Having mentioned the scholars' relevant opinions, Ibn Qudaamah said in Al-Mughni:
Having said that, cutting the hair and trimming the nails should be avoided. If one does it deliberately or forgetfully, then he has to ask Allaah for forgiveness, and he is not liable to compensation according to the scholars' unanimous agreement.
As for verbally expressing one's intention upon slaughtering, if you mean the provider of the Udh-hiyah or his deputy saying such statements as, "O Allaah, that is from You and for You," or, "O Allaah, accept it from me, or from so-and-so," then that is permissible. Moreover, Ibn Qudaamah said that many scholars recommend it.
Allaah Knows best.