Sad to say, not worth the effort!
However, if you are a bulk user of cable outer then you can invest in a big reel of the stuff (obviously genuine Shimano) and some Shimano cable cutters (TL-CT-10).
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Possible replacements
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However, order by Madison part code from your LBS and get the brake cable outers whilst you are at it.
The inners are easy to clean up, the outer liner erodes over time and no amount of blowing soapy water through shifts the detritus.
That part is the 'XTR' version, there is also a cheaper one that should work fine. !enter image description here
These are good, just so long as you don't cut mudguard stays with them:
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