Skimmer socks won't work if you don't have a skimmer. Basically a skimmer sock is a little sock that you wrap around the skimmer basket to help catch little stuff. If you have no skimmer, no need for skimmer socks.

You know what? I think if this was my pool that only held 1000 gallons, I'd just dump the water and start over. You are going to really struggle to clear it I think with no skimmer and most likely an inadequate cartridge filtration. Dead algae is most likely not going to be caught in that vac net thing.

Now that you know how fast an algae bloom is gonna start in your hot climate, just be diligent about chlorination so one can't get started. You've ordered the good kit which will hopefully arrive quickly and we can help you tweak things once you can test.

That is my opinion. What do you think?