This is a simple NO UMD FiX by pSyPSP, USA edit by vanhelsing:
1) Extract Worms_Open_Warfare_USA_PSP-pSyPSP to a folder on your PC using iSOBuster or similar utility.
2) From your original PSP_GAME\USRDIR move the DataPSP folder to the WORMS_OW\USRDIR folder from this pack.
3) Now follow the instructions as normal from the included NFO file:
Copy the 3 folders to your Memory Stick, boot Worms
in the menu. Press X (do not hit O to extract update).
Save works with this one fine.
Also, wifi seemed to work, this was not tested 100% though.
NOTE: Although this is labeled a "NO UMD" release, that just means you don't need the actual Worms UMD in the drive to play the game, however, you will need a UMD in the drive to run it (any UMD game should work).