I refoamed a pair of 12" infinity bass drivers last year and decided not to cut off the dust caps but to use an alternative method of centralizing the voice coil:

Once I had cleaned off all the old surround, I bonded the new foam to the speaker cone and allowed the joints to dry. Once dry, I marked the outer circumference of the foam surround at four points 90 degrees apart. I then rocked the cone to the limit of travel in the two planes and made corresponding marks on the basket and then split the difference and made four central lines, again on the basket. It was then a simple case of aligning the marks on the surround with those four lines. The speakers work fine at all volume levels and no voice coil rub.

Incidentally I found the best way to clamp up surround to speaker cone and to basket was using modern plastic clothes pegs with flat jaws, but obviously it has to be done one joint at a time.