Considering I often auto-swap stone axe and other tools from belt, don`t notice it and bravely go into combat with Frying Pan in hand - it would be nice to have some logic for *combat* tool or just dedicated slot/item in toolbelt that is equipped on start of the combat.
Simplest solution would be to pick highest-damage belt item as default weapon-swap when combat starts.
More elegant one will be to allow selection (through use of scabbard or dedicated toolbelt slot) of desired weapon. Weapon stored in such slot/helper item will be used as default on combat start.
Maybe make dedicated belt with reduced amount of slots but ability to auto-swap weapon in combat. That will create nice trade-off of having less slots for convenience of always having weapon in hand. Arrow quiver is using same design logic (convenience of arrow storage but loss of additional generic inventory space).
Though I can see how disadvantage of being unprepared for combat (and spending valuable seconds to weapon-swap) may be desired by developers.