For the cost of the cable, it simply is not worth reusing existing cable. It is so easy 99% of the time to simply barrel a 59 to 6, and simply pull it through. A two story fish replacement can be done in minutes. Rarely are this internal cables clamped. Easy to check, a person on eqach enad, pulling, is there felt tension? Even if there are a few clamps, often the cable in will just pop the cable from the clamp.
One hint, it helps, after you barrel the two cables together to wrap the cabel and barrel with tape to make it a smooth shape, plus it adds strength to the connection.
Some remove the connectors, strip the outter, shield and center insulation away. Twist the center condutors together, then securely tape. Makes the resulting joint even smaller if there is doubt about getting 'hung'.