neighbor Pam!
Were this my decision....I would chose electronic wire transfer but only from my bank to her bank...not a cash outlet. Western Union would be considered a cash outlet. There's probably others. Electronic transfer from her bank to the seller's would leave a detailed paper trail. The seller would've had to provide identification to open the account plus the buyer would have the seller's bank's routing number along with her account number.
If you are ever awarded a judgement against another individual...in order to collect if you aren't paid...you need to have the banking information.
I really don't find it alarming that the seller doesn't accept paypal...and most who do probably don't have any problem with it...but I can imagine the possibilities. Get the funds...ship puppy and then a charge back appears on your account. Not to mention the service fees...