How do I find compatible coax connectors if I don't know the type of coax?
Look through a table of RG type specifications and find the closest match you can for inner and outer diameters, also matching the characteristic impedance. Then search for connectors that fit that RG type.

Be warned that the RG specifications were developed a long time ago and AFAIK there's no new RG types being introduced since many years ago. So microminiature cable types may not be covered by any RG type. Which will put you right back where you started, having to check each connector datasheet or a selection guide for the range of i.d. and o.d. they accept.