advice needed

So, you're going to make an extension by disassembling an antenna and adding additional coax cable between the antenna and the connector? That will work, but you have to be VERY good at soldering coax.

The guts of the antenna are essentially a piece of coax cable, so you're going to be doing some splicing. The coax used in most of the cheapo rubber ducky antennas is very small and very, very, very, lossy. Any more than a few feet of the stuff is so lossy, that methnks you're wasting your time.

I think it's RG-178 which is 0.072" (1.8mm) in diameter. There's also

1.13mm (0.044") diameter cable if want really tiny. Just search Google for RG-178. Lots of vendors stock it.

Have you considered looking at the specifications for such tiny cable? At 2.4Ghz, the loss is about 4dB/ft. That means you lose half your power for every 9 inches of this cable. How far were you planning to run it?

My guess(tm) is RG-178 which I think (not sure) is the same as Mil-C17/093. There are also non-standard miniature coax cables available. For example:

Search Google for "mini coax" or "miniature coaxial cable".

Suggestion: Leave the antenna alone and just buy the extension cable.