Hey Mitchell, looking at your requirements written down (after talking at the space yesterday), I have a bunch more questions... Take no offense if they seem dumb, as often as not it's just things you haven't articulated yet.
* How many days do you expect the battery to last? - Rechargeable? USB or inductive (wireless) charging?
* Could the 3 LEDs be 1 LED in 3 colors?
* What happens when you switch the switch to "off"? Is it important that the data be retained? Does it need to keep track of which light was on, so that it can restore that state when power is turned back on? Is there a value to "turning off" beyond saving battery?
* How do you intend to get the data off the device? I'm betting on Bluetooth, but I could be wrong.
** If bluetooth, I'm betting on a smartphone. Given that, would it be a problem if the device was just a bluetooth button and light and all the brains was actually in the smartphone?
* Assuming that the button cycles between lights/colors, and I was switching from Light 1 to Light 3 (via Light 2), would it be intended to show Light 2 for 1 second during the swap?
* How much timer resolution do you need? How much duration? IE "Up to 3 days, in seconds"
* Would the user care about the actual date/time of each change, or is duration all that's important? (timestamp or stopwatch, basically)
* What would be the eventual goal for this design? Do you want one for yourself or are you trying to build something to sell? If the latter, what's your target price point?
The way I'm imagining this (as a product):
A simple wristband with a rechargeable Li-Ion battery (probably contactless, inductive charging) with a single red/green/blue LED integrated into a button. Pressing the button sends a trigger to a smartphone app (via bluetooth) that says simply "switching from blue to red", and the app on the phone does the actual timekeeping and calculations.
Depending on what holes you shoot in my theory with your answers above, we're back to any old fitness tracker or smartwatch, and the entire project could just be software for a Galaxy Gear (/selfinterest) or similar.
Hopefully some of this is helpful in refining your concept. I don't have a lot of experience with wearables or [microcontroller] bluetooth, but I know which end of an arduino plugs into the SCSI port. :)
--Kevin