The bog standard rechargeable batteries (750 mAhr) in our DECT phones are
starting to lose their ability to hold their charge: they indicate full
charge but the phone cuts out with "low battery" within a few minutes of
being taken off the charging base station, especially if used on
speakerphone.

Is there a problem with replacing them with batteries that can hold more
charge ie 750 mAhr. I presume the phone will still charge them at its
standard rate (though it may take longer to charge them).

I will go for branded (eg Duracell) rechargeable batteries.

I presume that if the original batteries are NiMH, I should go for that same
technology.