I am the director of nurses over several different prisons and jails. Most of our facilities have a small Segregation unit (less than 50), but since you have a larger one, I would recommend splitting the seg unit in half and documenting on them every other day. This would be 100 (more realistic). Or you could even split them up more on each shift and have days do 50 and nights do 50, etc. How you approach the inmate will determine how long it will take you. I DO NOT recommend your staff letting the inmates know that this is a requirement. Do not ask the I/M if he has any problems. Just look in on him/her and tell him you are checking on him/her. I'm sure you are aware if you ask them if they have any problems, they always do. If they are sick, they WILL let you know when you do your walk through. And I would still stick with your normal routines for sick call. So if one says he has a cold, your answer would be an instruction on the sick call process.
If all of your nurses will be consistent and not have this be a sick call walk through, it shouldn't take very long.
I try and schedule this kind of routine walk through on night shift. If you develop a good flowsheet, it shouldn't take too long to document it. None of the nurses will be happy to do it, but it is a requirement.
Hope this helps!