Will that second signer initialing these particular documents never have to digitally sign a document?
If the second signer will never have to sign a digital document with a full name, it's even easier.. Just make a scanned signature with a set of initials, and allow some extra room where initials appear in a document to allow for the digital signature flag. But realize that you're crippling the ability to digitally sign a full name name for other documentation.
I'm getting the idea that this is being done more for digital appearances than digital record for your second signer. Whether you put that digital signature down with the impression of a full name or just two initials, it's still going to be a full digital signature as far as Acrobat and Adobe Sign is concerned. The only question would be whether that signatory would ever have to sign onto documents with their full name in other situations.
Good luck,
Randy