A worsted is a bit finer than an Aran, heavier than a DK.
Knitting with worsted normally gives 20 stitches per 10 cm/4in in stocking stitch. Aran would give 18, DK 22.
With crochet, the hook size and stitch type will make a huge difference. If you use the stated hook with a worsted instead of an Aran weight you’ll have a more open fabric. That may be what you want, especially with a cotton.
Best advice to give is to do a sample of at least 15 by 15 cm / 6 x 6 inches. That will give you a benchmark of the stitch size, the amount of yarn used and the stiffness or drape of the fabric you’re creating.