When I was Manager at Petsfart, I would have my minions bleach the ornaments very frequently. In one sink I would have rocks, ornaments and plants soaking in Bleach and cold water. And in the other sink i would have the finished ones soaking in Dechlorinater and Hot water. I used anywhere from around 15ml of bleach per 20 gallons to 90ml. As long as long as I put in a bookoo amount of dechlorinater and hot water on them afterwards, I was fin. Make sure and smell them when you think the're done. There should be NO bleach smell.
Letting them dry out in the sun works also. I would do this if my employees were slacking and ALL of the ornaments needed cleaning. One full day of the algae drying out and dying in the sun with a quick scrub or pressure wash and your good to go.