if dry storage at room temperature, then a grease-proof paper (butter sheets is an example) is preferable.
if dry storage in cool conditions (refridgerated or freezer), then glassine is good.
The bonus of glassine is that one can instantly see the specimen without having to unwrap - so less handling overall.
There is a major downside to both glassine and grease-proof - one has to write the data on the envelope with a permanent ink.
I will use newspaper or thin paper (40gsm) for field caught / papered specimens that will be curated back in the lab within a week or two, because the paper can have the data written on in pencil - no chance of ink runs or smudges or pens running out of ink in the field.....