Are you aware that it is rather easy to de-pin the connector. Also the JR male (plastic)connector will fit the Futaba female (plastic) receptical connector. The JR connector is smaller as it doesn't have that awful polarity flag. (The polarity feature on the JR connector are the beveled corners. With the connector housing removed it should be easy to run the lead down that tube. I like to use the largest wire I can. This is to minimize voltage drop and noise on the lead. So go with 22AWG.
P.S.
I like to keep the servo to extension connector in the area of the servo pocket. This makes it easier to replace the servo when they become stripped. I choose an extension lead long enough to reach the wing connector block or the receiver. I rarely if ever do I solder my servo leads and extensions. Aloft sell a set of loose pin plastic housings and crimping tool to make your own custom length extension leads. FYI: If you do solder your extension leads try to stager the splices to minimize the bulge.
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