Answer:
Thank you for your inquiry! The Miraclesuit Extra Firm Control Body Suit with Wonderful Edge comes with removable stretch straps, so it can be converted to strapless! It should definitely not make your hips "stick out more," since it is designed to give firm control throughout the midriff, tummy, hips, and rear. Since you wear a 38DDD minimizer, I would suggest getting a 40DD, which is a sister size. I've attached a similar style with a longer thigh line below.
If you would like some options that are more true to the 38DDD size you could consider trying a strapless bra with a body shaper! I've provided some pieces for you to consider below. The Spanx Super Control Higher Power Brief High Waist Panty and Chantelle Sensua Strapless Underwire Bra can be worn together for similar control. The Chantelle Bra comes in the 38DDD, and you can find your size in the Spanx Higher Power Briefs based on weight and height.
I hope this helps! Feel free to contact us with any style and fit concerns at (877) 728-9272. We would love to help you find the shapewear that perfectly compliments your outfit!