iMac Trade-in

If you can boot to recovery mode (or put your old Mac in target disk mode) then you can use Disk Utility to secure wipe the drive. The option is in the Erase disk process of Disk Utility.

Here's a link to an article on the subject from OWC/macsales:

How to Use Disk Utility to Securely Wipe the Data Stored on a Drive - eshop.macsales.com

If the drive is an SSD then this step is wholly unnecessary as SSDs don't store data the same way that magnetic media does and therefore data recovery is nigh impossible.

Your Time Machine backup is the best method to ensure you data can be restored. Apple likely won't even use the drive that ships back with the computer so there really is nothing to worry about.

The way I look at it is Apple is a 1 Trillion dollar company so they have pretty deep pockets and they have much more to lose by being irresponsible with your data than you possibly do. Your data likely isn't worth anything close to 1 Trillion, 1 Billion or maybe not even 1 million so you are NOT the one at risk, Apple is.