Changing the battery requires a basic knowledge of desoldering/soldering....easy stuff. After sourcing the correct stock battery type (with lugs attached) it's a simple procedure of unsoldering the old battery and removing it to installing the new battery and resoldering it in place. Great care must be taken to make sure the polarity is correct; the motherboard has a "+" labelled on it to help.
While I completely understand and respect that it's
your MP-1 and you can do with it how you see fit, it still begs the question: Why not just do the actual Battery Mod? It's the exact same difficulty (hardly any at all if you're experienced with a soldering iron) with the benefits of never having to unsolder the battery itself ever again, and to also use the easier-to-find coin battery without solder lugs like Richard said.
As for a video...somebody might have one out there somewhere.
I didn't make a video, but I did create the Battery Mod for the MP-1 and the writeup instructions will also apply to replacing your old battery with a new soldered-in battery. Follow the instructions up to the point of installing a battery receptacle, and just install the lugged battery instead while making sure the polarity is correct.