If you absolutely must have the latest PSP firmware, you may want to pick up Hot Shots Golf: Open Tee 2. The UMD comes packaged with firmware 3.96, although the contents of said firmware are unknown at this time. Considering the small numerical leap from the previous official release (3.95), we're assuming that the new firmware adds no significant new functionality.
We've contacted SCEA for a comment.
[Thanks, Shawn R.!]