How to Set a Custom Label for the Export Button in File Dialog?

Is there a way to customize the export button label in the File Dialog? Currently, the button always uses the bl_label of the operator, but I’d like to set a different label specifically for the export button while keeping bl_label unchanged for the F3 search. Is there a way to achieve this?

import bpy

class EXPORT_OT_TestExportOperator(bpy.types.Operator):
    bl_idname = "export.test_export_operator"
    bl_label = "I only need this label for F3 search but not for the export button"  # This text will appear as the file dialog button

    filepath: bpy.props.StringProperty(subtype="FILE_PATH")

    def execute(self, context):
        return {'FINISHED'}

    def invoke(self, context, event):
        context.window_manager.fileselect_add(self)

        # Attempts to override/change button label (this doesn't work)
        self.bl_label = "Custom Export Button"
        context.window_manager.operators[-1].bl_label = "Custom Export Button"

        return {'RUNNING_MODAL'}

def menu_func_export(self, context):
    self.layout.operator(EXPORT_OT_TestExportOperator.bl_idname, text="Test Export Issue")

def register():
    bpy.utils.register_class(EXPORT_OT_TestExportOperator)
    bpy.types.TOPBAR_MT_file_export.append(menu_func_export)

def unregister():
    bpy.types.TOPBAR_MT_file_export.remove(menu_func_export)
    bpy.utils.unregister_class(EXPORT_OT_TestExportOperator)

if __name__ == "__main__":
    register()