@hugo7 I just opened up the wireless button housing (which you need to do to change the battery anyway) then worked out which two contact points on the switch set off the doorbell when shorted and soldered two long tails to those. The other ends go to the contacts on the back of the brass button. Drilled a 4mm hole all the way through the frame and used a forstner bit to make a recess for the back of the brass button unit. The wireless button still works too.
I'm going to have a look at the inside of ours. Failing that I've found another that looks smallish that I'll respray black if we get a black door surround (still TBC).
Decided to tidy up the internal wires. I was going to sleeve them in white heat shrink and run them along the frame. But decided instead just to shorten them way down and mount the wireless button directly on the inside of the frame.
@hugo7 I just opened up the wireless button housing (which you need to do to change the battery anyway) then worked out which two contact points on the switch set off the doorbell when shorted and soldered two long tails to those. The other ends go to the contacts on the back of the brass button. Drilled a 4mm hole all the way through the frame and used a forstner bit to make a recess for the back of the brass button unit. The wireless button still works too.