Are you responsible for the other project as well? If you are, an option is to keep the resource's calendars at 8 hours per day and set the resource's max units to 50%. What you are saying then is for each project you'll get 1/2 of their time.

If you decide to stay with changing the working time for the resource calendars to 4 hours per day - the question about redefining the hours per day is up to you. If you leave the "day" to 8 hours and you assign 8 hours of work to the 4 hour per day resource - the duration will show 1 day but the task will start on one day and finish the next.

If you change the definition of "day" to 4 hours - the duration will show two days. Either way, you'll need to explain the definition of "day" to your audience.