You are probably better off quoting the Laws of Contract Bridge, 2014 Authorized Edition where Laws 68 through 71 deal with the proper handling of Claims and Concessions. Some pertinent aspects of the relevant rules are reproduced below:
Law 68 - Declarer's Claim or Concession of Tricks
.... Declarer should not make a claim or concession if there is any doubt as to the number of tricks to be won or lost.
Law 69 - Procedure Following Declarer's Claim or Concession:
When Declarer had made a claim or concession, play is temporarily suspended and declarer must place and leave his hand face up on the table and make a comprehensive statement as to his proposed plan of play, including the order in which he will play his remaining cards.
Declarer's claim or concession is allowed, and the hand is scored accordingly, if both defenders agree to it. ...; otherwise, if either defender disputes declarer's claim or concession, it is not allowed. Then, play continues.
When his claim or concession is not allowed, declarer must play on, leaving his hand face up on the table. At any time either defender may face his hand for inspection by his partner, and declarer may not impose a penalty for any irregularity committed by any defender whose hand is so faced.
The difficulty with creating your own penalty, in lieu of the official one, is that it can be difficult to apply uniformly from session to session, or even claim to claim. The Laws of Contract Bridge are an less formal statement than the Laws of Duplicate Bridge (for tournament play) and are designed for informal play by players who desire to play at a level beyond casual kitchen-style bridge. From your description this seems to be the atmosphere in which your group plays.