Since heat shrink tubing is often cross-linked through the use of electron beams, peroxides or moisture - the cross-linking helps to make the tubing maintain its shape, both before and after shrinking - the permeation characteristics will be less than virgin material. However permeation in itself is in most tubing application not of major concern, usually the degree of swelling and/or stress cracking causes mechanical problems on the relative short term. With this regard, a PTFE based solution remains a good option. At least as long as the material is not strained for long times and exposed to impact loads.
Below a link with some suggestions for manufacturers for heat shrink tubing (includes well-established companies like 3M, etc.):
Thorne & Derrick UK - Heat Shrink TubingSincerely,
Composite Agency