Would wearing this specific white dress to my cousin's wedding be improper wedding etiquette?

I appreciate your fitting dilemma, but this is definitely not right for a US Christian wedding. Look for something in a color and not so definitively evening. A clic simple navy, rose, emerald, purple, or even black would be a better choice. Try to choose something you can use more than once. You do not say if the wedding is day or evening and that also matters.