How can I watch movies directly from my external hard drive on my PS3 without formatting it to FAT32?

You can't, period. It MUST be formatted as FAT32 for the PS3 to read it, simple as that. Also, as Justice stated, the PS3 can't read MKV, they should be either AVI or MP4 for proper compatibility. And yes, unless you have your data stored somewhere else, formatting it (thus the term FORMAT), will erase everything currently on it. The only other way, as Justice pointed out, is to stream from PC using media server software such as PS3 Media Server.

The PS3 can only read drives formatted to FAT32, and it cannot read MKV files at all. MPEG, MP4, M4V, and AVI are the main file types it supports for video. Formatting the disk would in fact erase everything on it. You CAN stream movies from a PC via the media server function but that requires a PC that's connected to the same network as your PS3. You can do it through Windows Media Player but there are better programs to use such as PS3 Media Server. http://www.ps3mediaserver.org/