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I'm not aware of any (accessible) tester in these ranges.

You could test by diluting your solution down to the ppm range using a syringe and a litre of clean water, but the uncertainty on the end result is probably too high to bring any usable information.

My best take on it would be to double check your dosage calculations, use reasonably clean water and containers, use proper chlorine generating products (not expired), and discard the solutions after 24hrs.

The impact of microbiology/chemistry in the water would only be in the ppm range, so the impact on a 0.05% (=0.5mg/L=500ppm) will be minimal (ie: even if 1-2ppm of chlorine get used up when preparing the solution, you'll still be close enough to your target, even more so with 0.5% solutions)