Migrating my iMac to a smaller MacBook Air with a support external drive

Jezza,

When you say it has water damage, please explain. Generally water damage is a death knell for computers so my assumption is the damage you are referring to is only cosmetic otherwise the MBA wouldn't work.

Rather than attempting to do this yourself I strongly recommend that you make an appointment with a local independent Apple Authorized Service Provider that can help you. Trying to do this over a forums isn't advised as you will need face to face communication to be clear and thorough.Don't take the computer to your local AppleStore, use an independent Apple Authorized Service Provider. If you don't know of any in your area please click Apple Authorized Service Provider Locator (AASP) & Genius Appointment to begin finding one. If you can please avoid BestBuy Geek Squad, I haven't found them to be terribly competent in the past. If you still cannot find an Apple Authorized Service Provider, give AppleCare a call and they can help you find one, to get that phone number click AppleCare Contact Info to find the phone number for your corner of the planet.

That is the path I recommend rather attempting a do-it-yourself approach.

Your migration will not be smooth. I STRONGLY recommend that you return the MBA and get one with the same amount of storage as your old Mac. Then please follow the steps below. If you do not heed this advice, I can guarantee your migration will be at best messy and at worst not having all of your data available to you!

When you buy a new Mac the easiest, quickest and most reliable method to migrate from the old Mac to the new Mac is to simply connect the old Mac's Time Machine External Hard Disk to the new Mac using a USB cable before you turn on the new Mac. You will likely need a USB A to USB C adapter, you can find them on Amazon for $10 or less. When you start the new Mac for the first time it will startup Setup Assistant (SA), SA will get to a point where it asks if you are migrating from another computer, select Yes  and follow the on-screen prompts and it's done! It is THAT simple.

If you have already done SA on the new computer then simply connect the Time Machine External Hard Disk using a USB cable and launch Migration Assistant (MA) which is located in Applications - Utilities - MA. Then follow the on-screen prompts. 

The ONLY difference between MA and SA is MA will create a new user account that you need to log into.

Both SA and MA migrate applications (not 32 bit apps), data files & settings. They do not migrate Mac OS itself. Some professional apps such as Adobe and Microsoft apps may require re-installing their apps as they will not allow them to be migrated. As long as you kept the security keys for installing their apps, it is not an issue. 

Finally, never EVER use Wi-Fi when doing Setup Assistant or Migration Assistant. Why, it simply fails in most cases. Please read and follow the directions in Setup Assistant and Migration Assistant. If you do not have a Time Machine backup of the older Mac then create one! If you are not aware of Time Machine, please read Back up your Mac with Time Machine and finally if you need an External Hard Disk to use as a Time Machine External Hard Disk then many experience users on these forums prefer the OWC Mercury Elite Pro due to it's reasonable price, high level of quality and ease of use. 

Your welcome and good luck!