Is it permissible for me to recite the Mu'awwidhat without uttering (Qul - "Say")?

Reading the Mu'awwidhatayn occurs in two situations:

First: As a form of supplication (du'a). In this case, there is no harm in not vocalizing the word "Qul" (Say), just as a person in a state of ritual impurity (junub) may supplicate with Qur'anic prayers, or as one may supplicate with the Qur'an during prostration, without intending it as recitation. This was clarified by Sheikh Ibn 'Uthaymeen.

Second: As a form of recitation (tilawah). In this case, it is obligatory to adhere to all the words of the surah (definition) without addition or omission, just as the Prophet, peace and blessings be upon him, used to do when going to sleep, where he would recite the word "Qul" in both of them. This is also because the Prophet, peace and blessings be upon him, commanded the recitation of the two surahs in their entirety.