Prep cole slaw: combine shredded cabbage, mayonnaise, vinegar, sugar, and salt and pepper in a bowl. Mix until fully incorporated. It can be made a few hours in advance from serving sliders (keep refrigerated until ready to use).
Remove pork from the packaging. Pat dry with a paper towel. If the meat contains the fat cap (firm white fatty layer on top), remove with a sharp knife.
Combine paprika, cumin, salt, garlic, and chili powder in a small bowl and mix. Rub pork all over with dry rub.
Place in a slow cooker and pour cola or pineapple juice over the pork. Cover and cook on low heat setting for 6-8 hours, or high heat setting for 5-6 hours (until the meat easily pulls apart/shreds with two forks). Shoot for an internal temp of 200°F.
Remove the whole roast from the slow cooker and place in a large dish or foil pan. Remove the bone and shred it using two forks until in manageable tender chunks.
Add BBQ sauce and a few spoonfuls of juices from the slow cooker and mix. Prepare each slider with pulled pork, 1-2 spoonfuls of coleslaw, and 1-2 dill pickles. Serve pierced with a decorative toothpick.