Did this yesterday without removing the alternator, used a 1/4" drive ratchet with a short 10mm socket fished between the belts. Removed the belt cover and set it aside to gain a little more room. Thankfully, the bolt broke free very easily and the CPS came out with little to no effort at all.
Having smaller hands helps as you have to two-hand (finger) the securing fastener and then pop it out of the holder. I left the wiring connected and wiped off the end of the sensor, it too was covered in a black dust of sorts.
Fired the car up and it caught sooner than normal. It also used to have a bit of a stutter in the revs and it's smoothed that out as well. All in all, 30 minutes from hood up to hood down. My car has 110k on it and has been a west coast car all it's life (till now) so that may have alot to do with it.
Kudos to the OP, a worthwhile thing to do.