What does a AA battery marked with R6P mean?
The R6P can have a slightly higher voltage than the LR6.  The LR6 can supply more current than the R6P.  Either would most likely work fine in a wireless mouse or keyboard as the current consumption isn't too high.

The Wikipedia article on battery nomenclature explains the letter codes.

In this case the L prefix designates a specific chemistry, while the P suffix designates performance levels of the plain R6 type.