There is the wall hammer I doubt you have one if it has buds as these don't normally bud.
There is the parra ancora from far north WA and NT, this is the easiest to deal with the buds. Though as yet to see an orange one.
Then there is the QLD varient I call kidney bean hammer. This has larger vescules and is usually a solitary head, with the buds around the base. You possibly have one of these?
If so they are slow growers so buds will take several years to reach any size rather than months with the Parra ancora. I have some toxic green now 20-50c size fully expanded after 5 years growth. These were grown from such buds.
If you try take them too soon likely to fail they need to stand proud about 2.5-3mm from the coral to have a good chance of releasing them without crushing the structure. And yes it is certainly better to go for the ones away from the area covered with skin, though if big enough you can succeed with them.
You cant hurt the parent unless you over handle it during the process, best to only handle the dead portion of it and try keep it under water if you can.
The main points are to remove the bud without crushing and then not to use to much glue. The best way to remove the bud is to catch the very base with some fine pointed and thin blade pincers or scissors, but do not cut rather just give the gentlest of tweaks to one side to snap it off. Attempting to cut will likely crush the corals structure 'terminal'. To attach use the tiniest amount of glue and handle the bud ever so careful with tweezers. Be extra careful as you let go the bud it does not tip into the glue, keep it vertical.
Good luck with the opperation
I'm keen to try and grow one for you.....
anything happening?