Press the top and lay it flat on floor. Is the edge of the quilt wavy while it is laying flat? If the edge is already wavy you are going to have more waves after adding the border. Lay the border fabric along the longest side and see how much extra border fabric you have. Check the other side and see if it is the same. Place pins at intervals along the sides easing the extra fabric as you go. Put the top to the feed dogs as that will also help ease in the extra.
Will you still have a wavy border? Probably but try quilting it in a bead board design to use up the extra fabric and use an extra fluffy batting to disguise the extra fabric.