New housing is the best way to go. It's not particularly expensive, so adds little cost to the project. The new ferrules and fresh housing, which comes pre-greased, yield such benefit (and peace of mind) to the job. It's the right way to do that particular maintenance. The cutting and prepping the ends of the housing can be successfully accomplished in so many ways--the most common and best ways are outlined in others' answers here--with common household tools. It's difficult to accept any rationale for making do with old housing over new cabling.
If you must proceed on that route, inspect the old housing for damage such as bends or cracked plastic. This is especially common at the areas around the ferrules. If such damage is noted, it should be repaired by trimming off the damaged section and replacing the ferrule. We're back to square one now, eh? The ferrules themselves can be a common source of excess friction as the ends where the internal cabling comes through become distorted and develop sharp edges as the hole becomes reamed out by the internal cable. Any burrs should filed off and make sure the hole is such that it doesn't interfere with the passing of the new internal cable. Again, replacement of the ferrules is best practice, yielding exceptional benefit for very little cost.
External cabling that is to be reused is best flushed with a Teflon (PTFE) containing spray such as TriFlow or specialist sprays by Liquid Wrench or specialist WD-40 (not the regular stuff which is more solvent than lube and dries out quickly actually leaving less lubrication than before). The TriFlow or specialist sprays above come with a little application straw which can be held on the end of the housing (removing the ferrule helps get more spray through the housings lumen than if left on. Flush using short bursts and continue until the spray dripping out the other end is not discolored by dirt and rust particulates. Note any areas of excess friction when you pass the new internal cable through the housing and evaluate if it needs replacing. There should be no resistance as the internal cable slides through the housing. It should slide smoothly through the length of housing. You may encounter a hitch when the end of cable gets to a ferrule, but once through, the housing length should slide smoothly back and forth on the cable. This is a good time to flush your shifters with the Teflon spray as well. I hit the derailleur's linkages too. Wipe off any excess spray after giving it several minutes to work in and it's carrier solvent to evaporate.