Back to the original post - the Park in the pic is a hideous price (although the magnet is useful to extract loose balls when servicing a hub) - there is an easier way with internal cables.
1 - get a length of gear cable outer about 50 cm longer than the longest internal run you have in the tubes.
2 - strip off the outer casing and the longitudinal wires - and end up with a very the thin tube plastic inner
3 - disconnect the inner cable you are replacing at the tube exit (for a rear mech that could be at the mech if the cable goes in the stay)
4 - thread about 15cm of the inner to be removed into the plastic tube from 2
5 - gently feed the inner cable back from the other end of the tube, making sure it takes the plastic tube with it
6 - when the plastic tube emerges from the frame remove the redundant inner cable
7 - to fit a new cable feed it through the lever/shifter and feed the first 15cm into the plastic tube
8 - gently feed the new inner through the fame tube until it emerges
That's it - simple - no messing about chasing with the magnet. If the frame has the outers in the tubes (some don't, but have stops at the tube entry/exit points) then just fit the inner and then slide the outer along the inner back through the frame tubes.
... if you look on YouTube there are several films that show how to do it .... and keep the thin tube for next time.
Rob