The thickness of the pad is .114" but for cabinet doors the Don-jo #1608 would not be the correct model. The Don-Jo 1609 as seen here is correct for wood applications:
But the thickness of the face on this model is .140"
Don-Jo does have a shelf adhesive model available with the part number 1610 as see here:
But that is 135" thick.
The only item that comes to mind that will approach the 1/16" thickness requirement would be a self adhesive felt pad.
Is there a follow up question that we can perhaps attempt to answer? We take pride deep in our technical expertise, as we know it separates us from our competition, so don't hesitate to ask.
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