You can definitely find scrubs with just a drawstring, they're usually cheaper than the ones with elastic. I'm not really a fan of the scrub material, I have no clue why my classmates say they're comfortable enough for PJ's, but they do come with just a drawstring. I've actually found the scrubs from
Walmart to be the most comfortable fabric, they're the softest anyway. I buy the ones with an elastic in the back at least, because otherwise they fall off me, but I've seen without also.
Have you considered maybe just pulling the elastic out of a pair of sweatpants and leaving the drawstring in?