Micro-sized powered LED
Some of the inputs you seek:

Battery:


Smallest commercially available button cell: SR416 Silver Oxide, 4.8 x 1.65 mm, will just about fit your 5mm diameter cylinder.
Note: Just 8.3 mAh capacity. You might need a stack of them, and 7mm height of cylinder leaves just about room for 4, depending on what else takes up vertical room - see below.


On-Off Toggle switch


Look at AT42QT1012: at 3mm x 3mm x 1.45 nominal dimensions for the SOT23-6, this is a touch toggle switch that also works in proximity sensor mode with no additional capacitive sensor required. The UDFN package is even smaller, if needed.


PCB


DuPont Pyralux AC should serve well. Flexible, etchable, thin and flexible.


Battery Life extending tricks


Run your LED at half or less that its rated current, by adding an appropriate SMD resistor: it will still be visible enough.
Use a red LED, they have the lowest voltage requirement of common visible LEDs. If you want to have multiple colors, a bigger enclosure is a good start, for the MCU you would need in there.
Flash the LED instead of keeping it on - a triple-flash of 0.05 seconds or thereabouts, on-off-on-off-on-off every second, ought to be sufficiently noticeable.
This last would have been a no-brainer option if you were already incorporating an MCU in there, but probably worthless in your current constraints.


I hope this provides sufficient input for your project, and then there are the datasheets.

Do report on how it turns out!

A question I could not resist asking: WHY?