Tape will not do the job.
Several layers of glued heat shrink tube ( it comes with glue & without glue, guess which is the cheaper one ) over the top after a few punches with a fine centre punch some times works
But the cost of the tube is more than a replacement universal cable.
A cable maker should have ferrules of the right size to rip yours off and fit a new one but most of these places have a minimum charge and again that is less than the price of making a new one
Not familiar with your machine but usually a choke cable is clamped tight at the carb end and some times at the control end as well
The outer only needs to be clamped in one place to stop it moving.
What generally happens is the inner rusts solid to the outer so way back when it started to become stiff, you were stretching & compressing the outer rather than moving the inner through the outer if the clamp is tight
If not you were moving the entire cable and the clamp has fallen off .
The throttle cable on the HRC mowers down here are notorious for doing this because the cable run is poor so the cable must be lubed regularly which no one ever does
You need to remove the cabe both ends then try to move it back & forth to check it is running through the outer and the best test is to grab on end with pliers & try to rotate the inner without the outer moving ( cut finger warning applies )
If the inner is actually free you can buy "Bowden Cable Ferrules " from cable suppliers but they generally come in bag sizes of around 100 which again are more expensive than a replacement universal cable .
All real mower shops will have rolls of replacement cables some might even keep ferrules, if not push bike shops may keep them