If you are changing the first flight on the ticket the fare and taxes must be recomputed. The "reissue" fee is not from OW (that is free), it must be a T/A fee. It sounds like you are changing the first segment in which case you will have to pay any new taxes/fees such as the fuel surcharge for any of the 20 segments. Re-issue after the first segment is flown will not incur this except for any changed routings (at least other fees work this way, not 100% sure if the fuel surcharges don't have special rules).