Since I'm lazy, but I (a) firmly believe the Braves should trade essentially any player over thirty whose name doesn't rhyme with Bar? Take us!, and (b) want to speculate on where those players may go, as well as for whom they might be transacted, I thought I might deploy the traditional lazy-man's gambit and crowd-source the research.
So: who needs the parts the Braves have to spare (working under the assumption that any player not controlled past 2016 is "spare"), and with what might those teams reasonably part for such parts? By my estimation, the following could (and, almost to a man, should) find themselves in other uniforms by August:
Position Player Interested Teams C AJ Pierzynski White Sox (?) 1B/OF Johnny Gomes 1B/2B/3B/OF Kelly Johnson Zombie Expos (?) 3B Chris Johnson Giants, White Sox 3B Juan Uribe Giants, White Sox RHP Jim Johnson Mariners, Blue Jays, Yankees RHP Jason Grilli Mariners, Blue Jays, Yankees, Red Sox LHP Luis Avilan Blue Jays
Then there are some additional cases: guys like Luis Avilan, who's controlled through 2018, but will be arbitration-eligible soon and could be too expensive for what he's worth by 2017 (or may have perished as a result of Fredi-induced exhaustion); or Cameron Maybin, whose resurgence heretofore may propel him into Atlanta's longer-term plans, but whose contract and good play might combine to make him a swell candidate for a plum trade; or Eric Young, Jr, whom I can't imagine any team valuing unless they want to strategically break an opposing pitcher's ankle, but you never know. It's also possible Cahill pitches well enough in relief that he draws a desperate team's attention (though I'd assume the Braves would have to offset some salary).