i agree lets not connect going up to har habayis with putting a note in the wall! ones a minhag- and ones a possible issur karais!
The rambams account of going up- is not so simple- " There are those who assert that Rambam davened on Har HaBayit. This is based on an autobiographical letter attributed to Rambam about his travels in the Land of Israel (see Yitzchak Shilat, ed., Iggerot HaRambam, vol. 1 [Jerusalem, 5747], 224-226). However, the letter’s authenticity is questionable. Even if Rambam wrote it, his reference to Har HaBayit is somewhat vague. Some recent posekim—primarily those opposed to ascending Har HaBayit—suggest that Rambam davened in a synagogue located near, not on, Har HaBayit (Minchat Yitzchak 5:1; Tzitz Eliezer 10:1:54-55, 11:15:6). See Rabbi Goren, Sefer Har HaBayit, 350-351.
Not so simple.
I agree the minhag to put a note in the wall is---a minhag--- the mitzva of giving tzeddaka----Mitzva deoraysa. So i propose you fullfill a mitzva deoraysa and fulfill a minhag for $5. Seems to me that its a win win!
You propose- Giving it to someone going to har habayis. 1. possible issur karayas. 2. Assur by many ( including non chariedi rabbonim see list on bottem) even if you know the measurements for others reasons such as making the place open, so people who are tamei might come up. 3) Putting yourself in possible danger (deoraysa). And more and more and more....
In my self promoted opinion - my idea is a safer bet!
p.s- i myself only put a note in the kotel once- to fulfill the minhag. But i have no problem doing it for others if it makes them and the tzeddaka happy!
List of non charedi/ or charedi light rabbanim who forbid entry to har habayit:
Rabbi Yona Metzger, Ashkenazi Chief Rabbi of Israel (March 2012)
Rabbi Shlomo Amar, Sefardi Chief Rabbi of Israel
Rabbi Ovadia Yosef, spiritual leader of Sefardi Charedi Judaism and former Sefardi Chief Rabbi of Israel
Rabbi Eliyahu Bakshi-Doron, former Sefardi Chief Rabbi of Israel (March 2012)
Rabbi Shmuel Rabinowitz, Rav of the Kotel (March 2012)
Rabbi Avraham Shapiro z’l, former Ashkenazi Chief Rabbi of Israel and then Rosh Yeshiva of Yeshivat Mercaz HaRav
Rabbi Shlomo Aviner, Rosh yeshiva of Yeshivat Ateret Cohanim
Rabbi Yisrael Meir Lau, former Ashkenazi Chief Rabbi of Israel and current Chief Rabbi of Tel Aviv
Rabbi Yitzchak Weiss, the Minchat Yitzchak
Rabbi Eliezer Waldenberg, the Tzitz Eliezer
This is also the position on Rav Avigdor Nevensal (March 2012), Rav of the Old City and Rav Aharon Lichtenstein of
Yeshivat Har Etzion