DynamoDB error on UpdateItem - Item size to update has exceeded the maximum allowed size

As per the documentation, max item size is 400KB.

My update code is as shown below,

try:
    ddb.update_item(
        TableName=ddb_table_name,
        Key={'id': {'S': str(id)}, 'ts': {'S': str(ts)}},
        ExpressionAttributeValues={':b64msg': {'S': str(b64msg)}, ':stat': {'S': str(res_dict['st'])}},
        ExpressionAttributeNames={"#e_id": str(e_id), "#stat_1": "st"},
        UpdateExpression="set #e_id = :b64msg, #stat_1 = :stat"
    )
except Exception:

Here, the "b64msg" is a binary blob which is more than 4K.

So does this error means, we cannot have a key's value be more than 4K?

Is there a workaround (other than splitting the value to multiple KV pairs) to put a value of more than 4K in Dynamodb?