ICOT, the text of the award speeches are available online. They simply don’t mention the Korean conflict at all. The speeches mostly discuss the Camp David accords, and also mention his work monitoring elections & fighting disease. I’d guess that the “promote economic and social development” phrase, which is taken from the Carter Center mission statement, is a reference to the latter.
I do agree that the timing of the award was politically motivated & intended as a jab to Bush. But it had little to do with his work in North Korea, which as you noted was in 1999. (Though it may have had to do with his trip to Cuba earlier in 2002). Rather the timing of the award had more to do with the run-up to the Iraq war. In September 2002, President Bush addressed the UN assembly about Iraq’s biological weapons; you may remember that the war was not popular internationally. In fact, Congress authorized Bush to go to war against Iraq the same day the Prize selection was announced.