There are 2 methods to turning a normal PSP battery into a Pandora battery. Hardmodding, and softmodding. The alternative is to buy a Pandora (such as the Datel TOOL).
Hardmodding is as you just discovered - opening up the battery, cutting one of the wires, and you're done. Hardmodded batteries are Pandoras that can't be reverted, except by using some graphite (pencil lead) or something like a copper wire to bridge the gap you just made. This is one option available if you have 2 batteries but only 1 PSP.
If you only have access to 1 PSP (as in, your friends don't have PSP or at least not with CFW), most here would say it's best to just buy the Datel TOOL. It's a Pandora battery you can buy fairly cheaply, and doesn't require cutting up your own battery.
If you have a friend/relative who owns a PSP with CFW on it, you can simply use their PSP to softmod your battery. That means replacing the tiny bit of code in the battery (I believe it was called IPL, although I forget) with that of a service battery (Pandora). The programs to do this usually have an option to backup the battery's IPL so you can revert it to normal later. A Pandora battery will force the PSP to enter "service mode" on startup (if it's bricked or working fine, it will always enter service mode so you can install CFW or OFW). From service mode, you can install CFW from the magic memory stick, and once you're done, you can use the same program used to create the Pandora battery to turn it back into a normal battery.
This is called softmodding because it only deals with software, and is completely reversible. If you follow the instructions (which isn't hard - Desparter del Cementario offers a step-by-step walkthrough - takes minutes to complete), then nothing can go wrong. The only exception to this is the TA-088v3 motherboard, which is currently unhackable. There are other topics for information on this, but only the very latest batches of PSP Slims will have this motherboard.
EDIT: Once you've got CFW on your PSP, then you can run homebrew, emulation homebrew, etc, to your heart's content.