I claim to be no expert I would not try to charge the mouse and cell battery at the same time. However this setup has worked great for me for recharging these old batteries. I have 1 of these batteries powering my keyboard for the last 30 days and only lost 1 bar of power, I got about 18 hours of power for the brass horse lamp before recharging. And keep in mind that these batteries are not new.
FOR SAFETY REASONS I SUGGEST YOU DON'T ATTEMPT TO DO THIS! UNLESS YOU KNOW AND UNDERSTAND BATTERIES AND BATTERY TYPES ALONG WITH CHARGERS AS I AM BY FAR NO EXPERT AND KNOW JUST ABOUT ENOUGH TO BE DANGEROUS.
Step 1: Tools & Parts
Solder & Flux
3.7 Volt Cell phone battery
USB Cable with male & female ends
Step 2: Soldering the USB to the Battery
1. Dab a little flux on the contacts if your wires are already tinned your good to go if not be sure to tin your wire before trying to solder to battery.
2. With tinned wires in hand carefully solder wires to battery.
3. Wrap some black tape around the wired side to help keep wires in place.
Step 3: The Charger
Step 4: Wiring the USB to the Charger
2. With your contacts identified dab some flux on the contacts and then solder your USB cable to the charger.
3. Replace the cover.
4. Plug in your battery for about 2 1/2 hours for a full charge.