I don't follow.
You said you don't want to patch, presumably because your flash cart or emulator setup is not amenable to such things. Personally I would get a better setup but play it how you will.
You now say you don't want to use cheats which is the other means by which it is done. In this case you would presumably find where the "currently selected character" value* is stored and then force it to be Shiva's when Zan's is picked** (don't know if the megadrive cheat options have conditional setups like that, it is mostly a feature associated with later systems) such that picking Zan sees you ultimately play as Shiva. Not as elegant as a nice patch that allows you to pick from the title screen but will get the job done.
Unless you are going to find a glitch within the code that results in another character being selected you are out of options.
*now I am considering a randomise on death/screen change setup here... that could be quite fun actually.
**for the unfamiliar then Streets of Rage 3 has some bonus hidden characters you get for defeating certain characters as the game goes on ( https://strategywiki.org/wiki/Streets_of_Rage_3/Characters
). Should you then have to use a continue you get to pick a new character, if unlocked then you have some extra choices beyond the base characters. As far as most fighting games (and racing games for that matter) are concerned though then a hidden character is just a normal character but with the menu unable to unlock it. Find what value controls the currently selected player character (be it from a selection menu or in the game itself, varies between games as to what is best to approach as sometimes the player value is not locked in by the menu until things are started) and force it to be something else with a cheat or something and you get yourself a hidden character, play around with the numbers (might need to try a lot of them, usually it is the numbers immediately before or after the normal players or at the end of the range) and that is typically how most "play as boss" cheats are made as well for it generally makes sense to have bosses use much the same code as normal player/AI characters.