This is just STUPID.
Looks like you're using carbon zinc batteries at the beginning, meaning really cheap and shitty batteries.
Two AA batteries will give you ~ 2.5v at 2800mAh ... AAA ones will give you around 1000mAh. You're replacing that with a 3.7v..4.2v 150-300mAh battery ... guess what's going to hold more charge.
The simple diode is not enough to protect the battery, at some points you're going to push more than 4.2v in that tiny battery and you're going to kill it gradually. At low currents, the voltage drop is much less than ~ 0.7v over the diode.
Also, those tiny batteries can't be charged fast, they need to be charged slowly at maybe 0.1-0.25C (let's say 100 mA) so it will still take hours to charge the batteries.
You solved one problem but you created another one - yeah, now you don't need to remove the batteries and install other batteries (a one minute problem) but now you have the mouse locked in one place (over the charge coil) for at least a few minutes until theres enough energy in it, to a few hours until the battery is fully charged.
Could have suggested something simpler... reuse the battery compartment for a lithium battery .. make a hole in the front or in the back of the mouse for a microUSB connector, use a 1-2$ usb charger IC to charge the lithium battery in the battery compartment when needed, directly from the computer. Optionally add a led or two to show battery full or battery empty.
You can still use the mouse when battery charges (it would just feel like wired mouse for a few minutes to maybe an hour while battery charges)