I can not give you a definite answer for this but I do not think this will not really make much of a difference. Your son may be reactive to the chlorine which is the basic ingredient in a pool system. The salt water pool still has to revert to chlorine. Eczema is a chronic inflammatory disease and may present with flare ups even after a long time. The triggers may be from the heat , the dust or the pool water . I would suggest that your son be washed thoroughly with a mild cleanser like Cetaphil or neutrogena after each swim in the pool. With regards to the salt water system pool, you may refer to an allergologist with regards to this for further advise.
I cannot swim in salt water pools due to the algaecide used. This is often copper based and causes exzema to erupt where I am usually clear of it. This also applies to any pool where algacides are used. Bromazine is also a cause of exzema.
I am allergic to multiple pool chemicals and have my own pool using UV sterilisation which does not require chemicals.
I have got to the stage where I cannot usually swim in public pools as I break out in horrible rashes or exzema.