You shouldn't be dying off of one grab against DK. He can combo you well off of a cargo up throw, yes, but he shouldn't be straight up zero to deathing you. DI his up airs up so it makes it more difficult for him to get them.
Also, Sheik can chaingrab DK starting at around 30% If they DI in it ends at around 90 but you also get crazy good followups if they do that. IT goes until 120 or so if they DI away, maybe even longer. Abuse that, especially on FD. You outspace him with your tilts and his only really safe aerial is back air. You also edgeguard the heck of out him because if you toss needles at him and he dips even slightly below the ledge, he's gone.
Your combo game on his is also nuts. DK is huge, which means it's easy to hit him with aerials and tilts. If he DIs in on your down throw, you get a few tilts into an aerial. At higher percents (90-100ish) you get sweetspot up smash. If he DIs away starting around 45 or so, you get dash attack into something else really juicy.
You have needles too. DK has no projectile. His shield is also reallllly bad while Sheik's is arguably the best in the game.
DK is fat and combo food for you. Abuse it to the absolute fullest.