It is not the chlorine that normally causes the problem, but chloramines, which are created as chlorine attaches itself to impurities in the pool.
Chloramines are removed by chlorine shock treatment.
Alternatively, you can sanitise the pool using Bromine, but Bromine and Chlorine cannot be mixed, so you would have to empty the pool, backflush everything and refill the pool.
The customer could look at ozone generation or salination (salt treatment) but these need large lumps of hardware to be installed.
For pool chemicals, I use John Preston Pools & Spas, 01772 882500,
www.johnpreston.info