The problem is, as Red said, he can just challenge. And even if he doesn't you'll be somewhat hard pressed just to engage him. The Prince flies and has a high leadership so no march blocking. If you can tarpit him something like 2-3 scar vets and a 6 diced Savage Beast would do it... but that's a lot to try and line up while the rest of his army is bearing down on you. Also note almost all the Prince you'll see out there are mark of Nurgle, so you'll be hitting on 5s at least, and 6s if he gets the Miasma spell off. Pyre
You don't need 4 cowboys. You just need one. Old Blood, Cold One, Great Weapon, Armor of Destiny, Dawnstone, The Other Tricksters Shard. He'll beat the Daemon Prince in combat all by himself. Problem is actually getting IN combat with the Daemon Prince.
Which is why you run 2. Give the 2nd one, Cold One, Great Weapon, Tricksters Helm, Talisman of Preservation. Either Oldblood can go toe to toe with anything that chaos brings. You can take out the chariots/chimeras if the prince is hiding. -Matt