Actually, it is not entirely true that algae comes from too much nutrients in the water, algae will grow in a clean pond that has no fish or waste just as well if not better than a pond with fish!!!! The fish will eat the algae too!
The blue dye will help block out the strongest spectrum of light that causes the algae to grow. The blue dye is very safe and many years ago I did use it, but it does not last too long and the filters will filter it out.
In nature, the water can be dyed naturally as in the case of my pond right now. Caterpillars are here and they are dropping potent little dung pellets that cause my water to turn golden color, and that is helping to block the strongest spectrum of sun naturally. My water is still very clear, but it can go quite golden this time of the year, but the effects only last as long as the caterpillars are there, but soon they will cocoon and be gone.
Also some of the rivers north of the 57th parallel {northern Alberta} have a brown color to them as the hard wood trees that grow along the waters edges cause the river to look brown and dirty, but the river is just that way naturally in some cases. You can get the same effect from large amount of peat extract, the water will turn a rich golden color as well, like in nature, as nature does provide a color for the water too!
A pond with no fish can still be filthy. I maintained a very large pond for a customer of mine that had no fish, but was surrounded by trees. The bottom of the pond was filled with leaves, which break down into the food that algae eat. The pond had a nasty case of some sort of carpet algea all over the top. I would not consider a pond clean just because there are no fish in it.