Spacecraft magnetic field measurements are frequently degraded by stray magnetic fields originating from onboard electrical systems. These interference signals can mask the natural ambient magnetic field, reducing the quality of scientific data collected. Traditional approaches involve positioning magnetometers on mechanical booms to minimize the influence of the spacecraft's stray magnetic fields. However, this method is impractical for resource-constrained platforms, such as CubeSats, which necessitate compact and cost-effective designs. In this work, we introduce an interference removal technique called Wavelet-Adaptive Interference Cancellation for Underdetermined Platforms (WAIC-UP). This method effectively eliminates stray magnetic field signals using multiple magnetometers, without requiring prior knowledge of the spectral content, location, or magnitude of the interference signals. WAIC-UP capitalizes on the distinct spectral properties of various interference signals and employs an analytical method to separate them from ambient magnetic field in the wavelet domain. We validate the efficacy of WAIC-UP through a statistical simulation of randomized 1U CubeSat interference configurations, as well as with real-world magnetic field signals generated by copper coils. Our findings demonstrate that WAIC-UP consistently retrieves the ambient magnetic field under various interference conditions and does so with orders of magnitude less computational time compared to other modern noise removal algorithms. By facilitating high-quality magnetic field measurements on boomless platforms, WAIC-UP presents new opportunities for small-satellite-based space science missions.