Do the workd's favourite airline not provide a hand mike solely for the PA?
In a word on the BA 777s -
no, they do not have a dedicated "PA only" handmike (it may not even be a customer option.)
At the risk of teaching granny, etc, the hand mike (there is one), the headset boom mike and the oxygen mask mike all have their output "directed" by the MIC buttons on the Audio Control Panel...in other words you can talk on the R/T, or the Interphone, or the PA through any one of the three.... so get the selection wrong and we all know what happens....
The interphone handset on the centre pedestal does allow various PA options but to do that you have to faff around dialling the appropriate numbers which may not be the best/easiest option if you are wearing the oxygen mask.