We report a novel technique for side-pumping fluoride-based double-clad fibers, allowing a record coupling efficiency of 93% and a maximum power handling near 100 W at 981 nm. Our simple technique is based on wrapping a silica taper around a fluoride fiber and, therefore, does not require any complex fusion between these two dissimilar fibers. Under passive cooling, pump combiners made of undoped and erbium-doped fluoride fibers were successfully operated during several hours at respective incident powers of 91 and 44 W. Heat management issues and active cooling strategies are also discussed. This innovative combiner is a keystone towards the development of compact and robust high-power mid-infrared fiber lasers and amplifiers.