@Tugnoateng HNBR is okay for oil but might not bear high temperatures, we are looking for 200 deg C temp. range rubber
Jain AK, Rubber technologist
https://www.rubbersheetindia.co.in
Can silicone be blended/mixed with other elastomer such as nitrile to improve oil resistance properties.
Jain AK, Rubber technologist
https://www.rubbersheetindia.co.in
Vulcanized Natural Rubber of Shore hardness 40 SH "A" is generally used in table tennis bats.
If you need additional grip you can go for Rubber sheet with fabric impression on top.
Jain AK, Rubber technologist
https://www.rubbersheetindia.co.in