Is he really well asleep when you leave? My DD (2yo) will wake if she's not in a deep sleep when I'm leaving (then I hear "mama? mama? sit!" LOL).
Another idea, though it may sound strange, but could you incorporate the squeaking into putting him to sleep so that it doesn't throw him off as much when he hears it? Like if he falls asleep on his own, you can walk around the room and step on the squeaky spots occasionally or if you walk him to sleep then walk on those spots? Not sure if it's hard to get him to sleep though, if it is then you may not want to mess with it so it doesn't become harder.
I really sympathize though, I have in the past crawled out of DD's room on hands and knees to avoid waking her when we had a particularly sleepless night. Hope that mental image cheers you up a bit at least. 
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