The I2C is not the high speed link, but instead connects to a virtual EEPROM in the module that contains some fixed data (Manufacturer, model number, some other bits) and some variable data (Rx power, Tx diode current, some other stuff).
This a direct attach cable will not get it done, because that only sees the high speed links, but you may be able to hack a spare SFP to break the relevant signals out on some kynar wire.
If your switch has a QSFP port, you could maybe use a QSFP -> SFP adaptor and break the I2C out on that?
Regards, Dan.