I have an exterior painted wall and am interested in installing a stone veneer. I realize that I may have to install wire mesh to the areas but I'm wondering if there is a material that can be used to apply to the stone to the painted wall without mesh? Or should the paint be removed as much as possible then attach the wire mesh and apply a scratch coat?
You need mesh. While veneer is a fraction of the weight of full stone, it is not light. The mesh forms a framework that the bonding material will surround and be inseparable from it (absent smashing with a hammer). The mesh is firmly attached to the underlying structure with fasteners (type depending on the nature of the siding).
In this case, the painting of the surface makes no difference.
Getting mortar to adhere directly to an existing concrete, stucco, brick or stone surface is not simple, especially when there is a tendency of the attached material to pull away from that surface. Adding to a horizontal surface (like a concrete floor, steps or walk), there is mostly a compression force (pushing the surfaces together), and bonding makes more sense. On a vertical (or overhead) surface, where the force is tension (pulling away), this makes less sense.
I think you need the mesh.
A sand blaster is your tool of choice for removing the paint and leaving a good surface for the mortar to stick to.
Do note that one purpose of the mesh is to help hold the mortar in place while it sets up. It also helps to prevent future cracks from shifting.