You cannot"slide the new one in". At the lever end of the choke cable is a crimped ring, which fits over a pin at the bottom of the 'choke' lever. Also, if a correct choke-cable has been fitted, there is a crimped-on little collar at the lever end of the choke-cable outer, which is used to prevent the 'outer' from moving when the choke-lever is operated.
Unfortunately, the only way to renew the 'choke' cable is from inside the car. You will find the job a lot easier if (a) you have the rear of the car up on stands---high enough that you can work under the car and (b) if you remove one of the seats. Then remove the small cover-panel (on top of the central 'tunnel') just under the front of the rear seat. Before you remove the old cable, check where it 'runs' under the car. DISCONNECT THE BATTERY. The lever panel is held down with 2 x 13mm (headed) screws. Withe 2 screws removed you can pull the lever-unit clear of the centre-tunnel---this why you need to have the battery disconnected, because as you pull the lever-unit into the car, you will effectively pull the starter into the cranking position. carefully remove the pin from the bottom of the STARTER lever, and slip a long cable-tie or a piece of wire or string through the eye of the starter-pull cable (so that you don't lose it into the centre-tunnel). Doing this will enable you to pull the lever-unit out far enough that you can easily remove the old choke-able, and fit the new cable---again, note where the old cable went though the engine-bay bulk-head, just under the cover-panel. You will find that the 'inner' of the new cable is much longer than you will require---fit it into the carburettor, tighten the clamps for the both the outer and inner cables, ensure that the choke is being fully pulled ON and OFF, trim the inner to length. Use new split-pins, and refit all the panelling and the seat. Not a difficult job, just a mite tedious.