In practice there's no problem with the 2440 - just got 13 (!) hours running time out of my Garmin 25.
Charging circuits usually surveil voltage (which is the same for both batteries) - if the charging current is lower, it doesn't matter; just needs longer to charge, and the device handles this fine.
Settings during those 13 hours running time: Bluetooth on, two ANT+ Sensors connected, GLONASS off.
You can get the battery at here https://www.digikey.com/product-detail/en/illinois-capacitor/RJD2430C1/1572-1619-ND/6159137 ...the datasheet link is on the page ....I would stick with the original and not go to the 2440 ... charging current is higher and the battery resistance is higher.. the edge 25 circuitry is designed for the 110 mah battery...
Hi guys. I just replaced the internal battery on my Edge 20 and if you live in mainland Europe I can recommend a battery supplier in Berlin: www.akku-wechsel.de
I got good reliable service and the battery arrived within 10 days.....great.....!
There were a couple of issues, firstly, I used a T6 torx screwdriver which is incredibly fine and not a particularly common size. Secondly, the battery clip orientation inside the case is critical so take photographs. Thirdly, dust and other contaminants must be kept out as I had a small piece of invisible dust stop the Edge from working until I removed it. Good luck.