Ah, to override the texture, you have to do it through code.
If you're only using one texture, you can use MaterialPropertyBlock and Renderer.SetPropertyBlock
Texture texture = TheTextureYouWant;
var meshRenderer = GetComponent<MeshRenderer>();
MaterialPropertyBlock mpb = new MaterialPropertyBlock(); // cache this object somewhere. It's a reference type and it will alloc.
mpg.SetTexture("_MainTex", texture);
meshRenderer.SetPropertyBlock(mpb);
If you have to use more than one, you have to pass through SkeletonRenderer's override dictionary and create a new material object per instance.
SkeletonAnimation skeletonAnimation = GetComponent<Spine.Unity.SkeletonAnimation>();
skeletonAnimation.CustomMaterialOverride.Add(originalMaterial, replacementMaterial); // Do this for each material you need to substitute.