There is no way to engage our Webhook integration when you use Manage Buyers > Send free download link/code.
However, we can suggest an alternative approach that would work: you can set up a secret discount code for 100% Off the Cart Item Total, then use your own Add to Cart link along with that discount code to order the relevant item without payment through our Free Checkout.
To get that Add to Cart link n your E-junkie Dashboard go to Manage Products > Get Purchase Buttons/Links, select the relevant product from the dropdown menu at the top, then below that select the Cart button type, then under the Text Link provided there you can simply click the Open button to add the selected item to a shopping cart. Then in the cart you'd click the Add Promo Code button and enter your secret discount code for 100% off, then click the Free Checkout button in your cart.
During Free Checkout, you can enter the buyer's name and email if you have that, or just enter your own email and copy the link when you receive the email. You could also go to View/Download Logs > Transaction Log, find that Free Checkout order, click the Copy Link button for that order and paste the link into a personal message to the buyer (e.g. via eBay Messages).