We present a numerical study of a simple density functional theory model of fluid adsorption occurring on a planar wall decorated with a narrow deep stripe of a weaker adsorbing (relatively solvophobic) material, where wall-fluid and fluid-fluid intermolecular forces are considered to be dispersive. Both the stripe and outer substrate exhibit first-order wetting transitions with the wetting temperature of the stripe lying above that of the outer material. This geometry leads to a rich phase diagram due to the interplay between the pre-wetting transition of the outer substrate and an unbending transition corresponding to the local evaporation of liquid near the stripe. Depending on the width of the stripe, the line of unbending transitions merges with the pre-wetting line inducing a two-dimensional wetting transition occurring across the substrate. In turn, this leads to the continuous pre-drying of the thick pre-wetting film as the pre-wetting line is approached from above. Interestingly we find that the merging of the unbending and pre-wetting lines occurs even for the widest stripes considered. This contrasts markedly with the scenario where the outer material has the higher wetting temperature, for which the merging of the unbending and pre-wetting lines only occurs for very narrow stripes.