Automated transactions, which Nxt does not support, is one way of implementing atomic cross-chain exchange, but as you can see certainly not the only one.
Nxt does not support anonymous transactions, but it will support Coin Shuffling as described in this paper: http://crypsys.mmci.uni-saarland.de/projects/CoinShuffle/coinshuffle.pdf , here is the description of the Nxt implementation of it: https://bitbucket.org/JeanLucPicard/nxt/issues/135/coin-shuffling-monetary-system (note that it will work not only for Monetary System coins but for NXT itself too). The work as described in this issue is completed, what remains to be done is the so called "blame phase", making sure a rogue shuffle participant who tries to sabotage the shuffle is penalized for it. This will be released in 1.7.