So, after playing 10s for ages I am getting a bit lazy and would like to move to 9s.
Main reason: after discovering CtC I started practicing quite a lot, and my left hand can get quite tired after a couple of hours on `hard strings’.
Is anything horrible going to happen in terms of guitar setup? Or can I get away with perhaps rasining the action a tiny bit via the bridge thingies? My guitars are a Fender Strat and a Chapman ML1.
I have a Strat type guitar made by Carvin. Personally, I didn’t do anything when I tried 9s (I usually play 10s as well). But again, I don’t care about much as long as nothing is horribly wrong.
I have read that people usually check the intonation when changing string gauges.
I can’t confidently comment anything else.
I’m the same. I think it means we’re very rock&roll 
Rather than raising the bridge saddles I’d usually just tighten the truss rod a -tiny- bit, that will increase the relief in the neck which will typically reduce a little when going to lighter strings since they are exerting less force on the neck.
One big thing is that if you have a floating bridge, you’ll need to adjust the springs in the rear cavity (by turning the anchor screws counterclockwise some amount) in order to reduce the spring tension and get the baseplate of the bridge at the height you want.
Check out the very cool Strat setup series in the playlist below:
The heavier gauge strings bend the neck forward more (cause the neck to “bow”). Tightening the truss rod makes it work harder against that bowing in order to reduce the amount of “bow” and thus reduce the amount of “relief”. Lighter gauge strings apply less “bowing” force to the neck, so if the truss rod stays the same, it will be pulling too hard in opposition to the strings, results in less relief than you had with the heavy strings. In order to regain that relief, you will need to loosen the truss rod to accomodate the lighter strings.
Yup, sorry hadn’t had my coffee before I posted… you’re correct of course. Loosen to increase bow.
Good point, but you will have to LOOSEN the truss-rod. The truss-rod compensates for the force caused by the string-tension. As this force will decrease, the neck will bend backwards (towards a straight neck) or even going from concave to convex.
Change the strings, wait/play for a while. Press down the strings (e.g. the g-string) on 1st and somewhere around the 15th fret. there should be a little (I’d suggest something between 0.5-1 mm between the string and the frets in the middle, e.g. 7/8th fret). How much you need depends on how hard you pick. If there is less to no clearance, loosen the truss-rod nut a little (no more than a quarter turn at once) and let it settle for some hours or till the next day. repeat…
You can set the string action by adjusting them so that they don’t buzz when playing 14th-15th fret upwards. The neck is not affected by the truss-rod in that area. If it buzzes there, the action is set too low. If it doesn’t and it buzzes in the lower regions, its the truss-rod that’s too tight.
As long as you don’t do crazy stuff to the truss-rod, you can’t damage anything. It’s fun to also understand the mechainc side of the instrument.
Tom
EDIT: Sorry @Horganovski, I was too quick, already corrected. Nevertheless I’ll leave this quick guide here for @tommo.
Thank you Tom, this is a great concise explanation!!
After 20y or so of guiatr I’m finally beginning to understand how to do an acceptable setup 
I forgot the last step.
When you tinker with string gauge, the truss-rod or string-action, always check intonation afterwards, although others have mentioned that already.
As you stated, that your just starting to deal with the setup, a short explanation about intonation. Every time you fret a note, you also do a string-bend, just perpendicular to what you normally do. To compensate for that, you adjust the length of the open string. This virtually shifts all the frets in relation to the bridge.
I usually compare the fretted note at the 12th fret to the harmonic at the 12th fret. They should be equal. If the fretted note is sharp, screw the string-saddles a bit backwards (increase string length). If it’s flat, move it forward. Don’t forget to tune the open string/12th fret harmonic after every adjustment.
If your done, play a barre-chord at the 15th fret or up. If somethings wrong, you will hear it 