Storm door

I know of no way to do it without leaving a hole where the old one was. How adept are you with welding and sheet-metal working? You'd have to patch up the old hole, cut a new one for the new latch, install the new latch and then re-hang the door so that the return spring is mounted on the other side. You want to attempt all that?

Why not buy another new one 'cause it'd be better looking, faster to do and easier...even if it's not cheaper.

Wood was the original material from which storm doors were made. A storm door is a type of door that is installed in front of an exterior access door to protect it from bad weather and allow ventilation.