Q: replacement of power adapter plug without serial number?

I am pretty sure that the recall is for AC Wall Plug Adapters that "came with" your device(s) > https://www.apple.com/support/ac-wallplug-adapter/

Wall adapters do not have serial numbers so you don't need one to exchange them.

Sorry, what does this have to do with an iMac? The iMac uses a pretty standard AC cord. There is no "power adapter".

It has nothing to do with iMacs. I'm not sure that's all that important. There is a recall for Wall Adapters for iPads and iPhones so I would imagine the OP will be moved to a more appropriate place.

...

Exchange Process

Please choose one of the following options below. We will need to verify your Mac, iPad, iPhone or iPod serial number as part of the exchange process so please find your serial number in advance. Finding your device serial number is easy.

• Exchange your adapter(s) at your local Apple Store (Genius Bar reservation recommended) or an Authorized Apple Service Provider.
• Contact Apple Support.

Customers who purchased a World Travel Adapter Kit should use one of the options above to exchange their affected parts.

...

from the above link, and now here too > https://www.apple.com/support/ac-wallplug-adapter/

Sorry dufra. I don't know what I was thinking at the time.