If you want a swimming pond you either need to basically turn it into a pool with chlorine which would kill any fish or frogs in the pond and likely anything that drinks from it. This would be a bad idea if you have dogs that drink the water.

The alternative is to stock TP which should eat the algae but you seem strongly against a fish and swimming pond. Really all you can do is what you are doing, algicide and skimming.

0.7 acre pond stocked 2020, LMB, PS, YP.