Climbing in zero or low gravity is a -5 DC modifier. If the two objects are moving at high speed (let's say 300 MPH through outerspace, so no wind resistance), how would that impact the DC of the climb check?
It wouldn’t impact the DC at all
Two ships moving at similar speeds and similar heading aren't moving relative to each other any differently than if they were gently drifting near each other. Space doesn’t care about “speedometer” speeds, only relative speeds.
Climbing a cable between two ships travelling 300MPH would be the same difficulty as climbing a cable between two ships that are not moving at all: just the standard −5 DC for climbing in microgravity. It’s basically like them being parked beside each other. In fact, that’s exactly what they are: parked beside each other.
If this seems non-intuitive, look at any video of an astronaut taking a space walk from the International Space Station. That astronaut and the ISS look like they’re not moving. They’re not having any trouble at all moving around. But they’re both travelling at over 17 thousand MPH, yet it makes no difference* from moving at 300MPH or zero MPH, because they’re moving together.
* Almost no difference. The fact that orbits are curved has a very, very slight effect over a long enough time that makes them different from straight lines in deep space, but not different in a way that matters here.
As per my earlier comment, although there is no air resistance, two objects moving at high speed are likely not actually moving at exactly the same speed and course (although in game terms they are, of course, moving the exact same move speed). I would put the penalty somewhere between "severe wind" and "windstorm", so a +5 to +10 penalty. If an ally is on one of the ships, they could make a Piloting check against either an opposed check or a DC of 10. For every 5 they succeed by, they downgrade the severity by one rank, down to making it a +0 by keeping everything at a steady state. Of course, the same applies to failure or enemy action, making things more difficult.