I'll agree with the above suggestions that without fish or plants, you can go ahead & use chemicals to help prevent/treat algae. But! if wildlife uses it for bathing or drinking, remember that whatever you put in is going to effect them too.
Personal story (just for your consideration) At my previous house we had a 5' tall cement waterfall-looking fountain in our back yard that we were constantly having to clean due to algae & other muck (it was under large trees & much debris ended up in it) One day I put a single potted aquatic plant in it. Never again did we have to drain, scrub, clean or treat the water - that one plant took care of the entire problem (and, in my opinion, made it look nicer from a decorative point as well!)