Can I play Spellbound Caves in later versions of Minecraft?

I decided I wanted to try playing a CTM (Complete the Monument) map in Minecraft for the first time. I was told that Spellbound Caves was a great (and challenging) place to start.

I'm afraid that if I play it in a recent version of the game, however, that it will break the map in some aspect.

Is it okay, or should I play an older version of the game? If so, which version would you recommend?

It should be perfectly fine, Minecraft converts the worlds into higher versions so you can play back from 1.1 or so. Give it a try, but keep a backup of the world just in case, then work your way down the list of versions of Minecraft. Try latest 1.7.9 first, then 1.6.4 then 1.5.2