Possible to make refraction only affect background?

I have a material that has a varying refractive index (i.e. glass of varying thickness), and I would like to be able to apply a texture and associated mask atop this material (like a decal or sticker). Naturally, when I apply the refractive index to the material, the distortion affects the texture itself. Is there any way around this? I could mask out the areas where the texture exists, but the problem is the texture has a mask that is semi-transparent, and doesn’t have well defined edges, wheras the distortion is a well defined shape.

This would be easily solved by having two layers, the first being a refractive layer and the second being a masked texture layer. I have looked into this, but there doesn’t seem to be any way of blending two textures in such a simple ‘additive’ way.

I feel like this should be reatively simple - any ideas? Many thanks.