Based on this answer by Carl Woll, the syntax should be:

Cell[StyleData["Input", StyleDefinitions -> StyleData["Code"]]]

Setting the option programmatically:

SetOptions[
    EvaluationNotebook[],
    StyleDefinitions -> Notebook[
        {
        Cell[StyleData[StyleDefinitions -> "Default.nb"]],
        Cell[StyleData["Input",StyleDefinitions->StyleData["Code"]]]
        }
    ]
]

Checking:

As one can see, the input cell is formatted like "Code" cell, while in its definition it still has style "Input". Done!

Based on this answer by Carl Woll, the syntax should be:

Cell[StyleData["Input", StyleDefinitions -> StyleData["Code"]]]

Setting the option programmatically:

SetOptions[
    EvaluationNotebook[],
    StyleDefinitions -> Notebook[
        {
        Cell[StyleData[StyleDefinitions -> "Default.nb"]],
        Cell[StyleData["Input", StyleDefinitions -> StyleData["Code"]]]
        }
    ]
]

Checking:

As one can see, the input cell is formatted as a "Code" cell, while in its definition it still has the style "Input". Done!