You must select one weapon type which is symbolic to you.
This must be a one or two handed sword or mace. Not spears, staves, halberds or daggers.
Once this choice is made (and can never be changed) all future requirements of weapon ability will relate to that weapon.
All personages are expected to have/carry either a family weapon, or their own honour weapon.
They may only use this weapon when fighting duels.
How about something like that? It permits an aspirant to be more tailored to the style of the character, yet keeps a restriction in place, while adding a roleplay feel to it.
For example, the Templars often used two handed swords/hammers, so I think you can still be knightly without Having to use a one hander.