The rule of thumb for frozen milk is that as long as it's still slushy (partially frozen, but with some liquid) when it arrives, it's okay to re-freeze. Whether or not ice packs would keep it cold enough would depend on other variables - how hot is the weather where it's travelling, how much milk in the box (because the more frozen milk you have, the more cold it will stay), what's being used for insulation around the bottles of milk (crumpled newspaper is cheap & works well). . . Probably a small bottle of milk and a single ice pack isn't going to work well, but a tightly packed box with many bottles of milk & several ice packs would, especially as we head into fall/winter. Also depends on when you're going to use the milk - if it's still cold but not at all frozen, and you can use it w/in 24 hours, then it's likely fine.
If your donors are having trouble finding dry ice, they might try calling ice cream shops. Often ice cream is shipped w/ dry ice. It's usually cheap.
