Technically, בלעדי would work too, it means the same thing as בלי. But I hardly ever use בלעדי or hear it used unless with a pronoun: לכו בלעדי. נעשה את זה בלעדיה. etc.
What's more, I have never heard בלעדי used except for a person. בלי can be used for people or things, but בלעדי is only used for people.
AFAICT this is not in any dictionary, but you won't find any sentence with בלעדי חולצה
Does Hebrew have a -less suffix? Or is it the same for "shirtless" and "without a shirt"?