If you mean safest as far as maximizing profits and not killing cards.. I dont know if you have a mixed set of bins/banks or skimmed from one bank. I suggest you group them by bins and look them up. Then if possible take it to their own bank. For instance cash chase on chase. Why I say that is that not only banks have advanced flagging systems to detect any irregular activity, and you have more chances of pulling more from their home atm, but also the cards that dont have enough money, will still go overdraft (not in all cases) and they mostly do that on their home atms after you accept a fee disclamer. If its a small bank you can probably cash them in one go if limit is 700 you can pull it all at once and then find out where they are from and after midnight the banks time pull the limit again.
After you cash first time ...the limits you have some of them will die. To avoid taking out useless cards check them for validity I suggest classic method as suggested here before 1800jackoff (for us cards only I believe works). Only go out with valid ones (even though its a crap shoot, if the card doesnt have enough money to be authorized by 1800jackoff or any other merchant it will still say invalid when you could have pulled overdraft from atm).
If its a big bank and it flags cards for irregular activity, find out what the safety cushion is. Start with 300/pull see if it works well and increase it on the cards until you start getting problems. if 300 doesnt work well decrease it until you find it pays without block. Then you can try to pul the same amount again, or safest way is to wait couple of hours and pull again... a lot of pulls in short period of time most likely flags card.