Many people give their friends money to give to Tzedakah when they are traveling. The reason they do this is that it says "Shluchei Mitzva Ainom Nizakim". If someone is travelling to Eretz Yisroel which is in itself a Mitzva - or to do a different Mitzva is there still a need for Shliach Mitzva money?
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The Kaf HaChayim 110:27 says that one who is traveling should endeavor to be made a Shliach Mizvah. It does not mention money specifically.
Then it says that one who is not made an emissary should himself designate a coin and say that, Bli Neder, when he arrives at his destination he will, with G-d's help, give the coin to Charity in the honor of R' Meir Baal HaNess. (the Kemach Solet linked below says he saw this in the name of someone, but I can't decipher the name)
One of the sources for the Kaf HaChayim, the Kemach Solet (pg.121) brings Tzedakah as an example of Shliach Mitzvah.
From this it seems that making oneself any emmisary for any mitzvah will do, but if one is unable to become an emissary he should specifically give charity. Probably because Charity can save from death, as mentioned here.
Maybe we can derive something about this from the episode where Hashem tells Shmuel to go and anoint David, mentioned in the Gemara (end of Chullin and in a couple of other places) as an example of a shliach mitzvah who is not guaranteed protection from harm because קביע הזיקא - the danger is definite.
Shmuel is concerned: "How can I go? Shaul will hear about it and kill me!" (I Sam. 16:2). To this Hashem responds, "Take a calf with you, and say, 'I have come to sacrifice it to Hashem'" (end of the same verse).
So we might consider what Hashem's intention is with this last statement. Is it just to establish an alibi (and any other plausible action might have served the same purpose)? If so, then maybe it can't be much of a precedent. But if the idea is that Hashem is telling Shmuel to bring a korban in order for the merit of that mitzvah to protect him from harm - why, then, we have a case where a shliach mitzvah still needs another shlichus mitzvah for added protection.
[On the other hand, it may just be that this proves that an extra shlichus mitzvah which removes the קביע הזיקא is meaningful, as in this case, where taking along the korban would allay Shaul's suspicions. Where this is not so - carrying tzedakah money doesn't (in the natural order of things) make a trip any less dangerous - then perhaps it indeed doesn't make a difference, like in the case of the boy who climbed a rickety ladder to perform two mitzvos (also mentioned in Chullin loc. cit.), where the extra mitzvah didn't do anything to reduce the danger.]