The only real solution with 'squeaky' tapes is to find a machine they don't squeak on...!

Domestic and low-end pro machines have a felt pad to push the tape into contact with the head, and this is often the cause of the squeak.

Running the tape at a different speed (usually slower) from the original recording may sometimes work, but be careful for the reasons Richard mentioned above.

My 'safe' method is to use a pro 4-track (Teac 3440) which doesn't have felt pads, and will provide a signal from all four tracks simultaneously. It's also very gentle with the tapes, as the reverse bias (feed spindle trying to spin in the opposite direction to playback) can be adjusted.

This is especially good for tapes produced on a domestic machine, as you only need to spool the tape through once to get everything - admittedly some of the audio will be played backwards, but that's easily sorted digitally.