Normal laundry bleach is 6%, that works out to 60,000ppm, it'll sting after being on your skin for a while, if you rinse it off immediately under running water, I can pretty much guarantee you that you'd still have 100ppm left on your skin after rinsing.
Swimming in 10ppm is totally harmless, even 20ppm isn't a health issue - your kids will just come out pretty clean - the reason it's not advised is due to possible ingestion - even then, you need to ingest a lot.