Could you send me an audio recording of what the fan sounds like? I'm wondering if it's the regular hissing fan noise that is bothering your wife, or if the fan is making more noise than it should be.
Replacing the fan does require some amount of comfort with electronics -- you need to remove and later replace the CPU heatsink. That's because the fan is inside a "duct" assembly that's attached to the heatsink. It's all a matter of removing screws, but when you put the heatsink back, you need to make sure there's either enough of the original thermal paste there, or add some thermal paste to ensure that the heatsink is making good contact with the CPU. (Just to be clear: if your device starts malfunctioning after such a modification, this is not something we'll be able to help you with.)
I'm not sure how easy it will be to find an equivalent fan. The fan is a small fan, about an inch square, and it blows air to the SIDE, not top to bottom. (The air flows through the fan, over the heatsink, and then through the duct which directs it to the case vent. I'll send you a few pictures of the assembly and of the fan in email in case you still want to see what equivalent replacements you can find.
Re: CPU temperature and fan cycling ... I'll check, but I'm fairly sure we don't have any software control over the fan that would allow us to force it to run continuously instead of being tied to CPU temperature.