All babies are different but I prob had at least two cups of tea and one coffee daily with both pregnancies and after the birth and both DD and DS were/are far from hyperactive and good sleepers so in my opinion enjoy your cuppa, and only cut it out later if necessary.
Might just try and cut down to the one over the next couple of months and go with that then. It's only really if i have a coffee i notice she become quite active afterwards as well - maybe stay away from that.