Dr. Bronner’s?
Seems like I’ve seen a baby shampoo - maybe Johnson&Johnson, maybe not - with the magic phrase “fragrance-free” on the front label.
I think Dove shampoo is relatively low-smelly, although I haven’t used it in a long time and don’t remember it well enough.
Dr. Bronner’s might work for the OP, although I find it way too harsh and stripping for my hair. I keep a bottle around to thoroughly clean my hands - all the way up to my elbows, surgeon-style - for when I’m going to clean the fishtank. Also, it provides reading material in the shower. 