My best suggestion is to rinse thoroughly with warm water while massaging the scalp (to remove sweat), then apply a CLEANSING.CONDITIONER like WEN or Suave Rosemary Mint...this will cut down on the amt of shampoo applied to the hair, considering the fact you may work out several days a wk.
Then, you can do your regular wash with shampoo once a week, or however often. You may also want to include a mild protein conditioner after or before the cleansing cond, to combat the effects of sweat in the hair and to keep it strong after sun exposure. Sunscreen spray used on the body is also acceptable to use on the hair to protect it.
Though Im natural, I was relaxed nearly 20 yrs and during summer did workouts, lawn work, gardening in hot, humid South Carolina.
You could NOT prevent sweat from saturating your hair. The rinse well and condition regimen kept my hair clean and moisturized.
Too much shampooing will break off relaxed hair...and I should also mention I retained all my length, and was between SL and MBL over the years I used this regi. HTH!
P.S. I also use the same regi for my hair while natural and working out, but I follow the cleansing cond with a moisturizing cheap one, and sometimes a deep conditioning mask. I dont currently workout, but I live in NC where it is still quite hot n humid.
Most Black women here cant avoid sweating their hair out some unless its braided, twisted, shaven, or just in a natural 'fro.