Is the prayer valid by saying "Allahu Akbar" without raising the hands during the takbir, especially when suffering from the compulsion to repeat the takbir, which causes embarrassment and delays the prayer?

This is a whisper (waswasa) that causes distress and delays prayer. The religion of Allah is ease, so be present with your heart and be humble in your prayer at its appointed early time. When saying the Takbir, raise your hands and say "Allahu Akbar" once, and do not repeat the Takbir even if Satan deludes you into thinking there was a flaw. Raising the hands during the opening Takbir (Takbirat al-Ihram (definition)) is a Sunnah (definition) and prayer is not invalidated by its omission. Address the problem by completely ignoring the whisper, otherwise, it may lead to abandoning obligatory duties.