If the paper is too fragile for any liquid, skip the tea dye entirely and use Distress Oxide Sprays or Inks.
The Technique: Lightly scrunch the thin paper into a ball while dry, then smooth it out gently. Take a blending foam tool or dry kitchen sponge loaded with a rich brown ink (like Tim Holtz "Gathered Twigs" or "Walnut Stain") and glide it completely flat over the page surface. The ink will catch only on the high ridges of the wrinkles, instantly creating the dramatic depth of tea-staining with zero water damage.