However you will be doing it again at least every year, blue gelcoats just go chalky after a while. Paint is the better fix, one-pack easiest and cheapest, two-pack much harder to use but best. I've seen good results from brushed "coach enamel" paint, as used for old vehicles.
I didn't realise Lysanders were built in GRP - I thought they were all plywood, though yours clearly isn't.
The trick is to sand the hull with wet and dry using 1000 grit or more.
I tend to use 1500grit.
This cuts away the oxydisation really fast and cleans at the some time.
Then use a cutting compound as mentioned above.
I use G3 or 3m finesse-it, with a machine polisher, again as suggested above.
Keep the cutting head and surface damp when you cut and as slow as the machine will go.
Its easy to overheat the cutting head against the hull so keeping it damp also helps this.
I also use a permanent marker and scribble all over the area I'm going to cut, this helps me ensure I dont miss areas.
I tend to buff by hand with a clean rag initially and then the woolmachine buffer after, which keeps the wool buffer clean and more effective.
Its UV that oxydises the gelcoat so to stop it fading we use Farcela UV wax.
The Silverline polisher previously mentioned is a very good piece of kit. My previousw boat had a blue gelcoat hull, it was in the state pictured when I got it.