A length of 170cm is not all that long at all for I²C, but the concern with I²C is capacitance of the cable. The higher the capacitance, the higher the rise-time: the pull-up and the cable capacitance form a RC filter, which limits the available bandwidth. This is well explained in other answers, so I won't explain it all again.
This means that to reach a given bus speed, say 100kHz, so must either reduce cable capacitance or decrease the pull-up resistor. This is however a limit to how low you can reduce the PU, because low value requires increasingly large currents. I²C devices can typically handle >10mA just fine, but some devices may only be able to drain 5mA or so.
For HDMI cables, you will figure out that it is marginally possible to meet the target of 700pF with 2.2k resistor at 100kHz, because your PCB and devices also add some capacitance. You can buy HDMI companion chips that will provide high-speed TVS, 5V reverse supply blocking and more importantly an edge-rate accelerator for the I²C bus.
The edge-rate accelerator is basically a small circuit that checks the bus voltage. When the accelerator senses a rising voltage, it will enable a push-pull driver that will kick-in to drive the line hard. Likewise, a falling bus voltage will trigger that output to drive it low. You can buy such ICs standalone if you are concerned for your design. You can use LTC1694 or any other similar IC. There is a nice screenshot in the linked datasheet that explains it all on the first page.
The nice thing about those ICs is that you can add them in parallel to the bus. Therefore, you can add the footprint and add/remove them as needed when qualifying your design.
It is best to add them at both ends of the cable if you have a very long cable because the inductance of the cable would induce asymmetric performance, but for 1.7m, that shouldn't be much of an issue.