What is the best cheep pocket knife sharpener?

There’s a difference between cheap and inexpensive. One high quality Japanese water stone can cost $100 and you may need 3 of them for progressive sharpening. Tormek machines can run $300 to $800. There’s the Wicked Sharp kits and such that are hundreds of dollars. I’ve spent enough on stones and sharpeners, mini belt sanders, and gizmos that I could have just bought a Tormek T-8 out of the gate.
But in all my experience with sharpeners and to answer your question, I recommend the Spyderco Sharpmaker. You can get a new kit for $65 to $70. It holds the ceramic sharpening sticks at 2 different angles. You just hold the knife vertically and pull it towards you as the blade rubs against the stick on one side. Then you drag it across the stick on the other side. There’s coarse and fine sticks and you can purchase ultra fine sticks additionally. You can sharpen knives, scissors, serrated knives, & fish hooks. It stores in a small plastic case. It comes with an instructional DVD. This is the most effective sharpener / bang for your buck I think I have come across and the easiest to use. It’s not cheap. It’s inexpensive. It’s the best sharpener at a low price. Don’t forget to strop your blade for that polished, hair shaving razor edge. Good luck!

Wanbasion Black Stainless Steel Knife Set, Sharp Kitchen Knife