Just buy a self-adhesive stamp (no licking)...and use TAPE to seal the envelope...and as Demo said you can mail it from ANOTHER place not near where you live. Wrap the cash in several pieces of paper...or put it in a card. There is just no way they can trace you if you take those precautions. If you were really that adamant about it all...buy a cheap pair of surgical gloves to do all of that, no finger prints. How safe if that?
For the record...most posters who donate to GC do all or most of these things...although some of them do mail them from the state they live...of course those envelopes are completely destroyed, so the danger is non-existent.