The computer will “offgas” overnight so there should be no problem, worst case one of you might see mildly shorter no-stop time. Just don’t share it on the same day, that would actually be dangerous.
Try it yourself. Plan few dives, stick in 12 hours surface interval and see that it doesn’t really impact your no-stop time at all, not at these depths.
Same situation when you rent a computer from a dive shop - someone might have used it the day before, doesn’t matter.
If I were you, I would take an SPG too (get one without the funny console and clip it to a D-ring) and the second computer, in case that something breaks. Or at least the second computer as you could rent an SPG.