It's highly likely that the battery is fed into a voltage regulator that's converting it into something else anyway, and if so it shouldn't matter at all.  You could probably be several volts off even.  I can't guarantee yours is built this way though and take no responsibility for what you do based on this information though

well its a Logitech mouse so I would like to assume its well built, the only thing i'd need to remember is to not charge it if I do swap in a standard battery then

I suspect that regardless of how it's made, that much of a voltage change shouldn't have any ill effect.  I assume you mean you'd be making it 0.3v higher, but is that even the case?  If it's lower I can virtually guarantee it'll be fine as that is exactly what happens when you run any device expecting a normal AA on a rechargable AA.  It's been done on a huge variety of things for decades and I've never heard of issues.

Yeah it would be making it higher, the rechargeable battery says its 1.2v vs the 1.5v of the standard 

Ah I see.  Although if it's already designed with a AA in mind, then I'd be reasonably confident it will handle it with no issues.  I thought it was an integrated lithium cell or something.  If it's a standard AA receptacle they would have to assume people would put all sorts of AAs in there, including 1.5 v models.

Not sure why I didnt consider the fact that they most likely expected people to swap in standard AA batteries. It's a very obvious thing to do as well