Custom entity models (wheelchair)

Hey! As a part of a map I'm working on, I'm trying to create a functional wheelchair in Minecraft... My first attempt used block displays being teleported to an invisible horse, making the player be able to ride it. However it is rather buggy.
Id like to maybe use a texture pack to replace the horse model with a custom one + the texture... I´ve honestly never created a texture pack before, so I'm not really sure what this would require - ideally, would it be possible using only the texture pack, no additional mods or datapacks? (it doesn't necessarily need an animation or anything, as originally, I was going to settle with block displays...)
Thanks for taking the time to read this 😅