The Elariia line by Perlier sells a shower gel on hsn.com, type "Neutraline" in the search box. The body lotion does have a scent of cocoa butter. The two together are only about $4 more than shower gel alone. There are reviews on the website, very good Italian Bath and Body line, I use a lot of it. Can't vouch for how unscented the gel is, since I got the lotion and could smell the natural ingredients.
For myself, I use bar soaps like L'Amande unscented, sold at beautyhabit for $4 a bar, minus current discount of 25%, code DCHABIT. I do have dry skin.
At drugstore.com, do a search for "Dr. Bronner's" and you'll see an 18 in 1 Hemp unscented baby liquid castile soap for sensitive skin. My husband has never used anything but Dr. Bronner's liquid castile soap in all the years I've known him.
And if you have dry skin, exfoliate in the shower. Look at the Buf-Puf on drugstore.com, you can usually find those in drug stores or else use a loofah. Just wash with something like that instead of a wash cloth.
Another way you can exfoliate if you have dry skin is to make up a body scrub using almond, jojoba or vegetable oil and either salt or sugar, cheaper than buying scented ones, anyway. Scrub it on while your skin is still wet, then wash or rinse it off. It also works as a 60 second manicure, rub the scrub into your cuticles, then wash hands and go party! If you have cuts or scrapes, then use sugar, although it dissolves faster than salt. You can use the almond or jojoba oil without the scrub to moisturize, too - while you're still in the shower, smooth a little on while still wet, then towel off. Jojoba absorbs into the skin really well, but I am so dry, I use the almond.
PS Oil does not absorb well unless your skin is wet, so don't try that trick after you get out of the shower or you'll be all greasy. And welcome!!