Well you could let one of your other charcters join the guild and take the quest. If you then are a level 5 warriors guild member change that character to ranger class. It´s an easy quest! You can then buy the fletchery trait which will allow you to make more arrows. You just put that dragonarrow in the missile slot, arm him/her with a bow and you´ll have plenty of dragonarrows to go around.
If you can´t do this, post a message to Wyvern in the "Wyvern´s lost and unobtainable items" thread and she´ll get you a new arrow before you can say Gael Serran.