As a guy who does it for a living....
I would go the safe route and simply just shim. You do NOT have to replace the dustcap as the rumor goes. When I first starting messing with speakers, I found that it is possible to refoam without shimming, but the VC gap has to be huge so you have room to play around. Also, if its not right on center, then you have the risk of mal-forming the voice coil former at the extreme of travel when the edge of the former rubs against the magnet pole piece. its a rarity but it can happen. Then when trying to crank your favorite track with a nice drum snare you get a scratching noise in one speaker....ugh.
I will use a hobby knife / exacto and cut away the dust cap as close to its base as possible, leaving about 1cm still attached. I then flip up the dust cap, insert my shims and refoam. When the glue is done drying, I pull the shims, set the dust cap back down so that it sits right, apply some glue and use a very small weight to keep the dust cover there while it dries. Sometimes a very small tonearm weight is perfect for this purpose.
Just my thoughts.