There are three commonly available rechargeable battery composition types, and alkaline is NOT one of them.
The oldest kind, is the Nickel-Cadmium (Ni-Cd).
It has virtually been replaced in almost all applications because Ni-Cd has a tendency to take a "memory set," that is where it's usual usage, and that is generally being trickle charged, makes the battery to be very poorly responsive when you finally need it most.
The second oldest rechargeable in use has been the Nickel-metal Hydride (Ni-MH). This composition is much less prone to taking a "memory set." It still can have some small memory issues, but an occasional deep-discharge and recharge will usually correct that.
The newest commonly available rechargeable is the Lithium-ion (Li-ion). Li-ion batteries have been taking over just about everywhere except in high-current demand situations.
There are other makeup's based on these three basic compositions (using different electrolytes and polymers) but not trying to get too confusing here. Besides you can Google a search for anything you really want to learn about batteries.
The point here is that if you are trying to recharge alkaline batteries, while it might appear to take a recharge, it really doesn't. You'd almost get as much an effect by placing the alkalines in a warm oven (DON'T DO IT! It is too easy to have then accidentally explode - first hand experience here
).
Use Li-ion batteries for your application. They used to be much more expensive than Ni-Cd, but being so much more common now, the prices have come down. For your application, in a mouse, it would be the best of the rechargeable to use.