Okay, I figured out how to use a Sixaxis properly with this.

1. Do like >>11 said.
2. Install this: http://www.redcl0ud.com/controlmk/index.html
3. Start ComtrolMK and import the attached custom profile I built for Cave Story.
4. Configure Cave Story to use KEYBOARD, not game pad.

Here are the mappings:

Up/Down/Left/Right - duh
Select - Map
X - Jump
Square, L1, R1 - Fire
Circle - Inventory
L2, R2 - Switch weapons

The only thing not mapped to a button is the Escape key, to prevent accidental resetting/quitting; if you just need to pause; use Circle (inventory).