Wall thickness reduction, often due to factors like corrosion, erosion, or operational wear, presents a significant challenge in various industries. This study introduces an innovative solution in the form of the Staircase Magnetostrictive Patch (ScaMP) Transducer, a magnetostrictive patch transducer designed to generate a broadband pure shear horizontal wave mode within plate structures. The ScaMP exploits the influence of patch width on frequency response, resulting in a wideband frequency capability. This transducer is employed to estimate the minimum remaining thickness of a sample, leveraging the cut-off property of the wideband SH1 dispersive guided wave mode. Notably, the broad frequency excitation method using ScaMPT enables the measurement of wall thinning across a range of up to 80% of the nominal thickness with a single data acquisition. Experiments conducted on an 8 mm nominal wall thickness aluminum plate with gouge defects validate the ScaMP's broad frequency response, providing remnant thickness estimates with a maximum error of 5.5%.