One option would be to set up Unzip in a QL emulator, on your PC, and then transfer the unzipped files one-by-one via the serial interface. You would need an emulator that supports both expanded-memory modes and that interfaces to the serial port hardware on your PC.
Something like Q-Emulator [http://terdina.net/ql/q-emulator.html] would probably do the trick, though you need to pay for the full version to get expanded-memory configurations. If this looks interesting, you may wish to confirm that serial transfer works for you, in the free version, before getting the full version.
An alternative option is to buy a memory upgrade for your QL. I have a Trump Card clone, which I bought from SellMyRetro [http://www.sellmyretro.com/offer/details/10861]. It is primarily used as a floppy-disk interface. However, you don't have to plug a floppy-disk drive in: it provides a memory upgrade (a further 768kB) and ROM-based Toolkit II enhancements straight out of the box, which may be enough. Of course, if you go this route, you'll need to have a Microdrive cartridge with most of its sectors intact, to hold a copy of the Unzip program!
I should also note that I started out with similar plans to you, though after a couple of months, I decided to save up my money and get a floppy disk drive and more memory. It made using the QL much easier, plus I'm not totally reliant on Microdrive cartridges, which have variable reliability after 30+ years (though I am a big fan of the Microdrive unit and have a number of cartridges I use regularly (but that I back up to floppy disk)).
Let us know how you get on.
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