Various thoughts and approaches.
Different models can mean different things if there is different collision data associated with them, or abilities/weapons/whatever.
Anyway two main approaches I would look at first.
1) If it is just aesthetic and they are built using at least a similar enough underlying setup (copy, paste, tweak a few things being a common/expected development path) then you can possibly do a file overwrite/swap. Find the models/textures for the AI vehicles, copy-paste* over the stock ones and you have a possibility there.
*a better hack might relink things which is where you take the pointer to the original file you want to overwrite, and the one for the one you want it overwritten with (possibly plus any associated size data) and overwrite such that the original file is effectively leftover data and maybe two things are pointing at one thing on the CD/ROM/...
If you have some more file level awareness you might fiddle with some internals here.
2) Character selection hack, and more amenable to cheat approaches if you prefer those.
Many times the AI/boss characters/hidden characters/cut characters/... are left in code and use much the same underlying code as the player, however as there is nowhere in menu or in game to select them then the devs have no great concern about normal players winding up as those.
To this end character selection cheat time. It works much like anything else -- select one, search, change, search, change, search,... maybe with a leave it alone and search accordingly. Savestates can be useful here as well if you can't back in and out easily/quickly. What character gets selected might be at a menu when hovering, might be after you press go (including "are you sure" if that is a thing, might be after the last person selecting presses go, might be when the game actually decides to land in the level... (no real easy way of guessing I can think of, might as well try hover over first though). Anyway so you have the selected character value in RAM somewhere thanks to this search. Try other things -- bosses/ai/hidden/... tend to be numbers just outside the normal range (do make sure to check the whole range to see what goes -- if 14 becomes 16 in normal menu operations 15 might be a hidden skin) or right at the end of them (if most things are 8 bit values and between 0 and 17 then 255 and such like instead), though could be anything so if you have 255 possibilities and 14 normal players with a crash for anything but valid values... have fun checking all those (again savestates at a suitable point).
After this/if both those fail (including more file level aware approaches for the first) I would probably go for assembly based approaches, understand how the AI vehicle selection works and whatever and then adapt accordingly.
Marginally related and of minimal technical interest but I will link it as it is amusing
https://www.youtube.com/watch?v=-r-oaaWsPE8&list=PL15C9269E19F61DF6&index=23
Topic: [PSX] Rage Racer - A.I Vehicles (Read 656 times)