Thanks for the questions, glad to hear you like the blinky kits! Always nice to hear when someone has success with the programming.
The microcontroller in the blinky kits (a PIC16F1823) will run just at any voltage between 1.8v and 5.5v, however the max clock frequency changes with supply voltage. You can only use the max frequency of 32 MHz down to a 2.5 volt supply voltage. Fortunately, we are only running the blinky microcontroller at 16 MHz, which is a valid frequency all the way down to the chip minimum supply voltage of 1.8 (part of the reason we picked 16 MHz, actually).
The only other concern with supply voltage is the LEDs. The required voltage for blue LEDs is higher than for red LEDs, which is why we include a 3xAA battery holder (makes about 3.6-4.5 volts) with the blue blinky kits and a 2xAA battery holder (about 2.4 - 3.0 volts) with the red blinky kits. The blue LEDs we used are rated with a "forward voltage" of 3.3 volts, meaning you need to apply at least 3.3 volts to the LED to get it to turn on.
So it sounds like your 3.7v single cell lithium battery should work just fine even for a blue blinky kit, but will definitely work nicely for a red blinky kit. I'd say, full speed ahead! Let us know how it goes or if you have other questions about the conversion process (but it certainly sounds like you know what you're doing). Send us some photos and we'll even feature you on our blog!