You can add HTML img tags (linking to your social images) by manually editing your Mail.app email signature files. These will NOT show as an attachment on the recipient's email. Of course these will only work if the recipient's email client loads remote images.
The .mailsignature files will be in one of two locations depending on whether or not the email using the signature is an iCloud account.
If the account is an iCloud account, the .mailsignature files can be found here:
If the account is not iCloud, the .mailsignature files can be found here:
~/Library/Mail//MailData/Signatures/ (where is a version dependent on your current install, in Mojave mine is V6).
Editing .mailsignature Files
You may want to create a new signature (and associate it to your desired account). It will then show in these folders as the most recently modified .mailsignature.
Edit this file in a text editor that can view the HTML code (replace anything in the tags below the "Mime-version: ..." line).
For the simplest example, your file could look like:
Mime-Version: 1.0 (Mac OS X Mail 12.4 \(3445.104.11\))
<body><img src="http://www.example.com/remote_image.jpg" /></body>
Important Note for non-iCloud Accounts
If you're not using an iCloud email account, you MUST lock the .mailsignature files after editing, or they will be overridden.
Using the .mailsignature Files
Once you've edited the .mailsignature file, quit Mail and reopen. You can now select the .mailsignature you edited.
NOTE: Images from tags will not appear in either the compose window or in the Signatures tab of Mail preferences, but they WILL appear in messages you send (if the recipient loads remote images).