Actual climber here, dynos are a part of the skillset so I wouldn't necessarily include the jumping skill into the equation. Calling it a jump is pretty generous since a dyno can be in any direction and can cover anywhere from a couple inches to a couple feet. Also, it doesn't necessarily mean losing contact with the wall since 'dyno' comes from 'dynamic' and covers (in my opinion) a climbing move where your motion carries you through to the next hold and there is no option for recovery and retry. You either catch the hold or fall.
That means that a dyno is something you don't do unprotected (unless you're Dan Osman) and definitely don't do on an unknown wall (even Dan Osman), so is part of a
high climbing skill but it's absolutely within the realm of climbing. So you see dynos appearing in the climbing skill when the climber is either climbing casually and has protection and a lot of time to add bonuses to their skill in order to perform a dyno. The other time is when a climber is wanting to go fast (like you stated) and in GURPS parlance they would be using the 'Haste' option to take a skill penalty in order to reduce the time spent doing a task. Climbing certainly fits in this, so you can take a skill penalty in order to climb faster (same thing as spending less time climbing). Since individual climbing moves are below the level of detail of the skill use, 'going fast' here would include dynos probably. If you're not especially hustling, or even taking you're taking your time a dyno is still something that climbers do when it's the right move to make.
Also, Dan Osman had an absolutely ridiculous climbing skill.
https://www.youtube.com/watch?v=8e0yXMa708Y