I assume you are talking about moss not algae... If so it isn't actually dead when it is dry, just dormant... I wouldn't worry about it, if it were me, a lawn should shade it out if it is healthy, infrequent deep watering will help the grass over the moss, because the grass has long roots and the moss in non-vascular.
if you are in the US and want to use a ...
Use of UV for sterilizing water
vinegar for killing algae
I am familiar with these UV bulbs and systems for ponds, aquariums and hot tubs. You've got a good idea! But I couldn't find anything about killing algae on surfaces without water.
If you find anyone who tells you that your idea is possible, would you please let us know?
If I were you, I would ...