Those squeaks do show up in guitar Midi. Unfortunately they show up as freak notes because Midi can't recognize them properly. Transients from guitar are a big problem. The rule of 18 and its timbre verses piano notes.
You can actually edit them out in the piano roll veiw a lot easier than trying to remove them in audio.
Deminsion Pro has a very nice Martin Steel String sound in their included files.

ORIGINAL: spindlebox

I just thought of one thing reading this thread. Some MIDI-philes would KILL or pay a lot of money to have those squeaks in their "guitar" tracks.

Having some gives your music that organic feel that so much of todays recorded/electronic music lacks.

It's a great tip. Very true. I hate new strings.

Some pretty varied responses here, and many (not all) don't seem to really address your problem as it exists today. Here's what I would do. Use a Gate/expander. Set it to downward expand the squeaks, rather than cut them off entirely. Now, if the squeaks are so loud that you can't set a reliable threshold, then you can try keying the gate off of a cloned track EQ'ed (HPF and LPF) to isolate the loudest squeak frequencies. If one or two instances are being stubborn, use automation to nudge your threshold. Sometimes ya gotta step backward in order to step forward...