This clamp is being used on a piece of equipment that is a few years old. I am trying to identify the type of clamp this is. If you the reader cannot identify it, leave a comment with something similar that will not damage thin wire when clamped.
Ok, they look like the Kelvin clips on my cheap pair, which look identical to this one. Please note the insulated hinge found on both. Here is a set of clips from Amazon and one from Ebay. If so then you need to replace it with another Kelvin clip, like one of the following: Found at Amazon Found at Ebay AST Labs That is just a small selection.
It is identical to a Kelvin clip pair that I have. Mine have two coaxial cables and two BNC connectors per clip (so four in total for the red + black clips).
If you don't need the Kelvin feature (independent connections to each side of the jaws) there are plenty of small alligator clips.