Thanks, glad to hear you're enjoying it! The Tourist's Baton is his only melee weapon, yes. It can be upgraded with Enchant Weapon Scrolls, though.
However! It is a much better idea to stick to throwing rocks, daggers, swords, arrows, etc., as he inherently gets boosts to accuracy and damage in doing so. Resort to melee only when you can't / don't need to use the ammo.