The title to this thread does not quite match your post, so I am a bit confused. Who is the "instructor" in this case? Are you referring to an instructor who is going to be on this reef/wreck trip? $50 is a lot for a one day computer rental. If it's for a week, then it is reasonable.
You asked, "If I will be fine without a (computer)?" The answer lies in your training. Did you learn to use tables in your OW and AOW and do you have the equipment for tables? On the other hand if all of your training was done using a computer, then you are not qualified to use tables and it would be ill advised to not have a computer.
Attempting to "match" the dive profile of someone else who has a computer is also ill advised. If you are already back from your two tank wreck/reef trip and everything went "fine," please don't make the take away from your experience that you don't need a way to track your nitrogen loading with either tables or a computer. You need one or the other.