I agree with Robert that glue lined heat shrink is not a good idea as the glue will get soft and slippery every time the handle gets warm.
I wouldn't suggest an epoxy layer under the heat shrink tube, as there may be some chemical reaction between the epoxy and the heat shrink tube. Heat shrink tubes are mainly made from cross linked polyolefins, a long time reaction such as brittleness can not be excluded if they are in long time contact with other polymers, especially under elevated temperatures.
I would suggest to apply a heatshrink tube (or more then one) direct over the metal handle, or, if possible, produce wooden sleves which go over the handle.
Edited By Gerhard Novak on 27/09/2021 15:35:23