No you can't delete any mission. ( I am on Part IV of that mission, and it will be a while before I even try to finish it. Some thing to keep an eye on is that the amount of horseshoes you can pay to skip the food part will keep decreasing and just before you reach 50000, it will be 1 horseshoe. You can pay and keep your food.)
If you have a lot of missions you can use the mission manager in My Stuff to move it to the end of the line.