Archival paste is made of rice starch, at least the stuff I have is.
It should not add stiffness.

There is (or was) a glue that comes in a tube type applicator
called UHU that was acid free and would stick to more than just paper.
It even stuck reasonably to glass, so it would probably work on waxed
paper if it is the same as it used to be.  It seems to be a base of
rice starch but there is more than just starch in it.  It was made in
Japan.

I found UHU with Google and it seems that the old liquid tube type is
not made anymore but there are several acid free glues that might work
for labels on rolls.  The roller looks interesting.

Best regards,
Spencer Chase