Drain Li-Ion battery by connecting USB +5V and GND
There's two answers to this question:


Can it be done?: Probably not. Or in fact, very most likely not. To be a USB compatible portable device it has to not impose any voltage on the power pins by itself, unless triggered to be in host mode, which your watch very likely cannot do, because that mode was not designed into it. So you cannot access the internal battery through the USB pins.
Should you do it, even if you could? Again, probably not. If the battery is well protected internally it should be possible to drain it to a switch-off moment without causing deep-discharge and damage. But you do not know how well the battery is protected at the point your are "tapping" it. Maybe all the protection, not only sleep, but also safety switch off, is inside the watch's processor. Then tapping the battery directly will not include that safety and you can drain it to death.


Or to summarise: If you absolutely must, try getting the screwdriver, but since you don't have it already I might think you're better off taking it to some other place to be serviced.