Doesn't PlayStation need to be jailbroken in order to install anything without using the online store or actual disc? Itch will allow you to distribute the files, its more Sony that you have to worry about as from what I have heard and read about they really try to prevent people from sidestepping their marketplace.
You can definitely link to other marketplaces as redonihunter mentioned so your best bet is to get it on the official online store for that console and then just provide a link to that among your platform downloads. (besides, this will allow owners of that console to discover your game via browsing the online store which is much more likely to happen than for them to find it here...)