cork board of felt for use under a mantle piece sign?

I'm soon to be selling some stone signs that stand on a mantle piece/side board. Due to the weight I'd like to find something on thebase so as to protect both the underside of the stone and also the customers side board. There is a flat surface area measuring approx 35mm wide and 14cm long under the stand up sign but not sure if either cork or felt is suitable. I would imagine I'd need the thinnest possible hickness such as 1mm however if purchasing either with an adhesive backing would they even take to sticking on stone or would I have to apply further glue to the base. I'm looking for a really elegant finish so think black felt would look better, however so far can't find anything online that look appealing or are thin enough. Can anyone help?
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