Is it permissible to repeat "There is no might and no power except with Allah" with the intention of healing my sister who is sick with cancer, even though she can do it herself?

There is no objection to performing some adhkar (remembrances of Allah) and using them as a means (tawassul) to Allah for the fulfillment of a need, such as supplicating for one's sister. The remembrance of Allah eases difficulties, simplifies hardships, alleviates burdens, and removes distress and fears. Al-Hawqalah (saying "There is no might or power except with Allah") is one of the greatest adhkar in its effect on resolving difficult matters, enduring hardships, and warding off poverty, and it has an impact in confronting fears.