My Wifi router (or Helium Miner) has such a very small connector, about 5 mm in diameter. Is this connector available for every cable?

It is most likely an SMA connector. This connector is available for many cable types, including 10mm cables with low attenuation. However, you have to ask yourself whether it makes sense to run this from the antenna to the terminal. Often a compromise of a thick cable with common connectors (N-type) and the use of an adapter cable (pigtail) is more practicable at the device. The somewhat higher attenuation caused by this combination is then accepted.