Hi,
For prototyping I'm ok without a low power solution but I want to be sure this can be done before I start to spend more time/money into it. I've been reading about LiPo batteries and they look nice, high discharge rates and high power density. They even sell them in stackable thin films in various formats. The problem is that they look harder to handle safely but I think they could be a solution to my problem eventually. I've found this one for example:
It's very small (just 1mm thikness) and with 200mAh capacity, continuous discharge at 3V at 0.2C should give 40mA for 4 hours If i'm understanding it well. And with pulsed discharge who knows, there isn't info in the datasheet or I don't see it, but as a crude estimate with the info from the energizer cell that gave 7mA/0.2mA = 35 times more current (but pulsed) in the same time (more or less), then this would last perhaps 35 times more with the same 40mA but pulsed, or 140h.. again very roughly.. it isn't even the same technology. Also the pulsed data in the coin cell was for 2 seconds pulse X 12 times a day, perhaps not comparable with what a keyboard for casual use would spend (probably more).
Thanks for all the info, I'm going to buy the USB arduino plus the jy-mcu bluetooth module and probably also the one with the HID profile later.