Algae issues

[Authentic]

i have a small cyano breakout on a leather coral that was being eaten which has spread onto nearby rocks.additionall i have noticed alot of green algae on the frag base of my duncan coral.in that i can easily remove these pieces from my tank what is the best way to get rid of the algae without harming my coral?
last time i removed a piece with cyano only i burned it with a blowtorch/not connected to any coral.