The 'Character Exchange Ticket' form the Xmas Account gift cannot be exchanged: there is no option for it in Miyamoto Musashi's Item exchange (as it is specified on the ticket).
I also checked the other Miyamoto Musashi near the Zunda booths, and the other 2 exchange NPCs near the fountain (just in case the wrong exchange NPC was mentioned), none has an option for this.
I would have uploaded screenshots, but trying to 'Upload attachment' gives an error message 'Sorry, the board attachment quota has been reached.'.