Best bet is to find an old formula SAE car. While a little larger than a normal kart, they would be more in line with what you're trying to do. The one from where I went to school used the motor out of a CBR 600 fwiw.
Example
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'11 370Z Nismo #528 Fast Intentions | Stillen | Motordyne | Uprev | CSF | Zspeed | Z1 Motorsports | AST | Swift | SPC | SPL | Whiteline | Hotchkis | Bride | Schroth | Robispec | Cusco | Nismo | Volk | Forgestar | Hoosier | RJM
'17 Titan Bone Stock
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