Some conditioners will dull the shine on a Bal. Please don't use lubriderm, however many ill informed sales associates recommend it.
I love the shine, and won't buy a preowned bag that's lost it. Many of them do, just from wear and age. I can tell you that LMBs handle cream, For Handles Only, used to dull the handles. You might try that on an inconspicuous area, to see if it gives the effect you want.