Whisk shallot, lime zest, jalapeno, lime juice, orange juice, ginger, and salt in a small bowl. Reserve half of marinade for serving; cover and leave at room temperature until ready to use. Pour remaining marinade over shrimp in a medium bowl and toss to coat. Cover and chill 30 minutes.
Prepare a grill for medium-high heat. Grill shrimp until lightly charred and cooked through, 1–2 minutes per side. Transfer shrimp to a large bowl and toss with sesame oil; season with salt, if needed.
Serve shrimp with lettuce, cucumber, carrots, lime wedges, basil, sesame seeds, and reserved marinade for making lettuce cups.