Unfortunately, this is not the case. There are, in fact, a wide variety of BNC connector options. They are available in different sizes to fit 26 distinct types of coax cable. They range vastly not only in size but in coax wire type, signal protection and more than a few other factors.
Sorry Nick - I guess I could have offered a bit more info.
Yes - there are different wire termination types - but they are all the same standard bayonet type.
If we want to split hairs there are two distinct BNC connector styles , 50 ohm and 75 ohm. They are interchangeable but vary slightly in the insulation and shielding (dielectric).
I did not look but would assume that GHL uses 50 Ohm connectors, which are standard for small signal (audio, video instrumentation, etc) as opposed to 75Ohm which are more often used for higher frequency signaling (TV, Radio, etc.)
That said, given the application and signal, I think you would be hard pressed to measure the difference on a scope, let alone the ADC of the Profilux. Would be an interesting test.
In any case, for your purposes, this is going to be tough unless GHL chimes in and tells you what type of coax is being used.
What is going to matter is OD of the cable and OD of the inner shield and to a less extend the wire AWG (it is likely 22 or smaller) fits inside the sleeve of the connector. You will need to cut the old one off and strip the wire to get measurements or at least an idea.
You will need a crimp tool - using pliers may work, depending on the brand of connector.
Personally - I would cut out the bad section and splice the wires back together with a western union splice on the center conductor and cover it with electrical tape, then pull the shielding back together from both sides and tape that as well. Ugly but will be much easier than you trying to find connectors to match the wire and learn to terminate.