First I'd give it a shot trying to post here exactly what yarn it is and see if anyone has it. There's Buy/Sell/Trade forum here, too. And try looking for at at Ravelry.com - people are willing to sell/trade there too. and even try E-bay.
Could you re-do the whole border with the white? Then if you do die it and the border takes the color differently, at least it will look like you meant to do the border in a diff. color.
Good luck finding it - I'd definitely give that a shot first.