Grease and oil tend to collect dirt (although in a speedo cable I think it's actually worn metal filings) and stiffen up over time. Graphite won't do that and the irregular surfaces inside the cable tend to hold the graphite in place pretty well. A local speedo shop I have used also strongly seconded the graphite only philosophy.

When you pull your inner cable out look at it closely to see if it shows signs of wear. If so, and the wear is minor, you should be able to just replace the inner. If the inner cable has started to unravel (unlikely if it's still working decently) then you'll need to replace the whole cable. If the inner cable looks good just clean it up and relube with graphite.

This assumes of course that you haven't inadvertantly kinked the cable somehow doing some other repair. If that's the case you may be able to straighten it. If not it's time for a new cable (the whole thing).

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LRG
1987 300D Turbo 175K
2006 Toyota Prius, efficent but no soul
1985 300 TDT(130K miles of trouble free motoring)now sold