Scanning nanoscale superconducting quantum interference devices (SQUIDs) are gaining interest as highly sensitive microscopic magnetic and thermal characterization tools of quantum and topological states of matter and devices. Here we introduce a novel technique of collimated differential-pressure magnetron sputtering for versatile self-aligned fabrication of SQUID-on-tip (SOT) nanodevices, which cannot be produced by conventional sputtering methods due to their diffusive, rather than the required directional point-source, deposition. The new technique provides access to a broad range of superconducting materials and alloys beyond the elemental superconductors employed in the existing thermal deposition methods, opening the route to greatly enhanced SOT characteristics and functionalities. Utilizing this method, we have developed MoRe SOT devices with sub-50 nm diameter, magnetic flux sensitivity of 1.2 µΦ0/Hz 1/2 up to 3 T at 4.2 K, and thermal sensitivity better than 4 µK/Hz 1/2 up to 5 T -about five times higher than any previous report -paving the way to nanoscale imaging of magnetic and spintronic phenomena and of dissipation mechanisms in previously inaccessible quantum states of matter.