Hydroxychloroquine itself doesn't really do much at all to the virus. It's the zinc that does the work and a zinc ionophore (like hydroxychloroquine) allows zinc into the cell. You can use a different zinc ionophore like quercetin that can be purchased at your local vitamin store along with the zinc.
There's no great evidence Zn2+ is the mechanism by which chloroquine is effective, it's just a hypothesis.
Viruses like CoV are taken into cells by a process called endocytosis, which puts them in small organelles called endosomes (basically, think of it them like little cargo crates). Endosomes are then usually merged with other organelles called lysosomes, which are full of catabolic enymes that break down complex biological molecules like proteins - and which will also destroy viruses. Viruses must therefore exit the endosome before it merges with a lysosome. They then "hijack" cellular machinery within the cytosol (the general fluid interior of the cell excluding its organelles) to replicate.
The evidence we have suggests chloroquine and hydroxychloroquine do increase cellular concentrations of Zn2+, but specifically it localises
in lysosomes. This makes it unlikely that Zn2+ is interfering with the viruses, as it's in the "wrong" part of the cell. Furthermore, we can see from that same paper measuring the change in cellular Zn2+ uptake from 10-300micromolar, and the effects, particularly at lower concentrations, are modest. However chloroquine and hydroxychloroquine appear to be effective against viruses
at much lower concentrations, where the impact on Zn2+ entry is likely to be trivial, even if it were in the "right" part of the cell.
To get an idea how much hdroxychloroquine is in a cell from therapeutic treatment, mice on a 30mg/kg dose for 28 days showed cellular concentrations of hydroxychloroquine in non-liver tissues around
1-2 micromolar. The maximum tolerated dose of hydroxychloroquine in humans is about 1200mg a day, or 20mg/kg for a 60kg human; but 200-400mg doses are more likely (~3-7 mg/kg for someone 60kg) so around 5-10 times less than the mice in that study.
The first two papers (there is other literature out there along the same lines) are using cultured cell lines so there is always the possibility that human cells in vivo may be more responsive to the drugs in terms Zn2+ entry, and that there's more Zn2+ in the cytosol. But as there are other known effects of the drugs on cellular activity (specifically, altering the pH of organelles) which may be more effective, they look more probable.