Preheat oven to 400 degrees F. Coat a large baking sheet with cooking spray.
In a large bowl, combine chicken, sour cream, cheese, green chiles, cilantro, and cumin. Mix well to combine.
Arrange egg roll wrappers on a flat surface. Place a small amount of filling in the lower third (towards 1 corner) of each wrapper. Fold over the bottom corner of the wrapper, tightly roll up 1 turn and then fold in the sides. Dip your finger in water and run it along the corner and edge. Tightly roll up the rest of the way, sealing the edges and seam shut. Place "straws" on prepared baking sheet and spray with cooking spray. Bake 10 to 12 minutes, until golden brown.
Meanwhile, in a small bowl, combine honey, pickled jalapenos and vinegar. Mix well and serve alongside straws.