If the customer is planning to use WLC then yes all the AP's has to be converted from IOS to Light Weight (LWAP) AP. This can be done freely provided you have the correct software image. You should be able to download this from the Cisco site and you wont need to have a SMARTNET as long as you can get the images from Cisco site by other means:-)
Below url will guide you with the procedure.
Upgrading Autonomous Cisco Aironet Access Points to Lightweight Mode
Your AP's should be fine with the upgrades. AP1310AG has dual radio cards (i.e "A" which operates at 5GHz and "G" which operates at 2.4GHz). Your AP has only one radio (i.e "G"). Dual radio or single radio on a AP does not affect the upgrade procedure.