Clearing out accelerator tube question

[NeedAName]

Trying to install a new accelerator cable in my 1965. It broke at the carb end, pulled out from the front easily. When trying to install the new one it only goes in about 3 inches. From searching I've gathered that there is a red plastic sheath from the old cable possibly stuck in there.

So what kinda wire/metal tubing should I use to push it out? Any helpful hints?

Here's a picture of new vs. old end. New one seems to have the same diameter, just a little longer. Thanks for any help.

[vaughn bros.]

Here is a basic description of that little piece of tubing.
The tubing is red in color and says - "GERMANY 430-540-140D and measures 2.5 inches long, .187 OD.