Of course, this only works if you speak Serbian, and the panhandler does not. :)
I don't speak Serbian, either, but can do a halfway credible job of faking my way through broken, heavily Russian-accented English. "Da, tovarishch? Not really money you are meaning to be giving me to? No, no! Please! Not really now I am needing money some of now today, but most deeply now thanking you I am, nyet?" Shaking hands with them is... well, "another matter," I'll just say, and let it go at that.
Ha Ha Ha!
“Rushlish” is my fake language of choice in these situations as well...
Tovarich, Ya ne govoryoo pangliski, spasiba, da s’vidonyah!