Logitech diNovo Edge Wireless Keyboard Battery Replacement (Hacking with a BIGGER battery)

I have a Logitech diNovo Edge Wireless Keyboard for close to 9 years now its GREAT and has taken a lot of punishment but the battery life decrease greatly in the last week from 2 week on charge to 12 hours a charge (it was 3 mouths on charge when it was new) so I am looking for a new battery but cant find an Original Battery there are a lot of Compatible battery ? Should i go with them what do you think and from where to buy them ?

seeing how it is 9 years old, i'd risk a compatible battery. but i'd pay close attention to voltages and discharge values. i'd even mod it to fit a rechargable AA battery array(2 in parallel maybe?) if possible.

Non standard batterys suck. Check the reviews and get one. They generally aren't bad sometimes they don't hold a charge as well as an original but they tend to cost 1\3 of the price

This is want i think to do :
Because batteries for the keyboard cost 3x the price and i have to wait a month to receive it in my country I can get a battery for a phone (maybe s4) witch is even better 2300mAh (original is 950 mAh) and the voltage is the same 3,8 V and hack it with glue and some cutting/soldering ?
Will it work ? Will my keyboard EXPLODE and is there something else to worry about?

I bought a new replacement battery. I installed the new battery but it`s not charging. When I put my keyboard on the charging station its blink once green and after that it blinks red. I switch it with the old battery and it works so I was sure the problem was in the battery. I emailed ElectroPapa.com and received a second battery for free but it has the same problem...

My theory : The battery for the keyboard have 3 pins (+,- and T) and the "T" on my new batteries is not working properly so the keyboard protection decides not to charge them so I want to bypass the protection. Pictures bellow show my idea will it work, will it explode , what do you think I have to do? :-//

I made some photos hope they are helpful close up of the suspected
charger board on the keyboard and two photos of the insides of the
docking station charger.