WYSIWYG is more for wargear upgrades when you want shields or spears, it doesn't apply in this case.
The Hobbit rules do state that everyone comes with some form of weapon unless they are specified as unarmed, so we would assume that the archer carries a short blade of some kind. This means they do not suffer a -1 to win the fight (I think it is mostly just banners and 2H weapons which suffer this now).
Even though they are elves, they do not get an "elven blade", just a regular weapon, so they wouldn't receive any bonuses like those who pay for an elven blade - you'd think they made all their weapons the same, but no
Also, you can only use special strikes if they have that weapon modelled on.