Is a shop-vac adequate for discarding the greenish water on top of the pool cover?
A wet/dry shop vac should be great for this, and it will be a useful tool for the rest of the year as well.  The main limitation is going to be the amount of water you can "pump" before emptying the vac.  You'll be limited to 5-10 gallons at a time depending on what you buy.

Leaves or any other dirt or trash will be fine.  As long as it can fit through the nozzle and the hose, the vac will happily suck it up.  I've used mine to suck water out of a hole when doing an irrigation repair and to clean up a major water spill in the house.

Follow all instructions for wet use.  Normally the filter will need to be removed.  Also, clean the vac immediately and let it dry when you are done.  Old, dirty water gets moldy and nasty very quickly and can make the vac smell bad for the rest of its life.