With the caveat that this is not legal advice from attorney to client and should not be taken as a replacement for seeking the advice of a FL attorney:
I would strongly suggest shipping FFL to FFL because FFL holders are required to meet all sorts of standards that basically remove issues of criminal liability form your hands.*
If you contract with an FFL holder who then screws up, BATFE and FL LEOs will be knocking on HIS door, not yours.
*As far as knowing the age and eligibility of the purchaser, I strongly suggest looking at the relevant FL statute and making a sales contract that uses the statutory eligibility language - i.e. "I hereby affirm that I am over 18, not a felon, etc." You can email that and have the buyer sign, scan, and send it back to you, giving the buyer proof of your right to sell the firearm, and you evidence of knowledge of eligibility if the sale goes south.
Please do not rely on the above as legal advice. I am not your attorney, you are not paying me to advise you, I only practice in Indiana, and we have no attorney-client confidential relationship.