Palawan is considered to be one of the safest islands in the Philippines. Locals are incredibly friendly, patient and warm-hearted here. As with any destination, trust your gut and judge of character, follow the usual safety rules and the trip should go well.
Local men may say hello on the street and comment how beautiful you are, but the comments are non-threatening and warm-hearted.
Stay in touch with your hotel, use transport at night and keep an eye on your valuables: petty theft can happen like it does in most places.