I find the OP's plan quite practical, only one person is going to dive each day so only bring one set of gear, including one computer (as I understood the OP's post). As some of have said there will be no issue because with diving every other day each person will inherit the other person's previous day's profile. Which the net affect will be a move conservative profile for both while each will have a longer surface interval. Even if one person dives two days in a row the plan would be fine. Both people could dive on the same day and still be fine.
What I find more interesting is the numerous replies that state the OP's plan of using one computer would be risky or dangerous. The rule of not sharing a dive computer is true when both people are diving at the same time which will not be the OP's case.