yes you should be able to play all homebrew for 1.50 (pretty much everything) including snes9x. You will want the "snes9x 0.4.2 me" version (or which ever one is the newest) because it runs faaster and is only for 1.50 and OE types.
Edit: Here's how to get snes9x on your 3.40 oe
Download it here
Make sure you've got a GAME folder
Extract the contents with winrar
Open up the folder and go into the 1.5 folder
copy the two folders you see into the GAME folder
After that is done Make sure the kernel is set to 1.50. To do this reboot the psp and hold R. Recovery should come up. Go to configuration and set the Game folder homebrew to 1.50 kernel. Go Back and Exit.
Go to the memory stick under the game catagory and run snes9x TYL 0.4.2 me
You need to provide your own roms for the emulator. Do not ask for them here.