I mentioned TLS is in case you need the headers and such protected in addition to the mail body being encrypted. It's not a substitute unless you control all points between the sender and the recipient. Since you do have just the one recipient, connecting with TLS directly to the recipient's MX could be useful if it supports that standard. You'd still need to protect the message on the hard drives of the MX and spam filter/virus checking/IMAP/POP/mailspool servers and between such servers, which the end-to-end encryption of GPG is great for handling.

There are basically three ways to send a PGP/GPG encrypted message. There's the old inline way with ASCII armored data. There's the specific MIME+GPG way. Then there's the encrypt separately and just attach way, in which case a smart MUA might figure out the MIME info for the file on sending or receiving anyway. Since you want MUA support, either inline (for MUAs that use that dated standard) or MIME+GPG is the most likely route so your recipient won't have to save then decrypt the file as distinct steps.

Mail::GPG handles both the GPG+MIME of RFC 3156 and the older ASCII armored inline sending and reading of RFC 2440. That means it really shouldn't be a problem. You could even test both ways with your user's MUA.

Have you looked at the documentation for the Mail::GPG module? Is there some specific question you have about that, or some specific concern about how it may not meet your needs?