Take the broken teak pieces to a cabinet maker and price up a replica.
Alternate to no lock, you may want to consider a very cheap tiny lock that is easy enough to break but avoids damage. This way the non-professional is discouraged abut evidence remains if so entered, otherwise you may have sleepover guests that you won't know about. The depot and lowes sell these brass type locks in multipacks- keyed alike.
And leave any window curtains open which also allows the sun to keep the interior warm and dry. If you are hiding things, best to hide them out of site if feasible while still leaving the curtains open. What they see will be nothing, so they want nothing.
You may notice different size locks on dock boxes in any marina, I would guess the bigger the lock the bigger the bootie (?), even though every box latch is the same and presents little challenge to a wonder bar.
So, for two reasons both defeating the very reason for locks, avoid heavy locks if the latch is weaker to begin with.
