I'd suggest UV sterilization then, its appropriate for scale-up, as it is commonly done with large scale hydroponics. It should be easy to set-up in small-scale as well. The problem is, some organic carriers of important inorganic salts may be destroyed by sterilizing UV and precipitate out. This can be a problem with chelators for iron, the iron ending up precipitating on the submerged quartz sleeve. That said, you don't have to kill all microbes, just beat back the titer count of unwanted algae while your preferred ones flourish and crowd them out. In fact, I'd even consider filtration, you don't have to remove the smallest bacteria, just most of the blue-green algae. And for small scale, you can still autoclave water, transport it, then sterile filter your prepared seawater.