Whisk together mayonnaise, olive oil, lemon juice, Dijon mustard, salt, pepper, and hot sauce (if using) in a small bowl until smooth and well combined.
Drain and rinse chickpeas, then dry with a clean kitchen towel. Optionally, peel and discard loose skins for a smoother texture. Transfer chickpeas to a medium bowl and lightly mash about half of them with a fork.
Add drained tuna to the bowl and gently flake it apart.
Add celery, red onion, fresh dill, and capers (or olives) to the bowl.
Pour the dressing over the ingredients and gently fold everything together until well combined.
Let the salad rest for about 10 minutes before serving to allow the flavors to meld.