I don't know if this will help but I have only seen 2 types of connectors, the small white ones that connect to the motherboard that allow the motherboard to vary the speed, or a fan controller if you fitted one of them and connected it to that. Or a molex connector. If its a molex connector then it runs full blast all the time and if thats unacceptable then the only solution as far as I know is to replace it with a fan with the connector for the motherboard.
You might possibly be able to just replace the connector if you could source them but I've not tried this and am unsure as to whether this would work ok. Bearing this in mind I would just replace the fan with one for a motherboard connection (making sure first that there is one free of course).
Regarding opening the case to alter the fan speed can I ask how you do this if its connected my a molex because as far as I am aware it goes full blast all the time and cannot be altered?