Fresh water probably places greater stress on your skin. I know my skin radically wrinkles in a few minutes of tropical rain - but not in seawater.
I've been bathing in seawater for months. Usually by jumping in and out, or a bucket if underway. It's no big deal. I use cheap
shampoo. I prefer a quick fresh rinse in the ships fresh water to toweling of the salt water only because it saves laundry
work. Salty towels never dry and can get quite a smell going.
I have short hair so there's no issue there. Those with long locks will need a better rinse and maybe conditioners to get the feel they like. They may need a little fresh water for the shampoo too.
As for salt residue on the skin....that appears naturally by perspiration a few minutes after the shower
due to the constant heat and humidity of tropical paradise locales.
Sometimes I let the salt dry on my skin. Feels kinda nice. But I wouldn't go to the bunk that way as it can be a bit irritating where pieces rub.