The only 5v analogue circuitry I have is a capacitive sensor, on a 1M resistor, it's drawing so little power my multimeter couldn't even pick it up on its uAmp setting. Based on I*(9-5) = 0.08W, I reckon the linear regulator's barely going to get warm... as I have one here, that's what I'll use this time.
Thinking about the battery operated version; I'd do away with the "constantly on" LED, and I believe using level-triggered interrupts and sleep mode, it's possible to run a Mini Pro at around 6uA (while asleep obviously... when woken it will take the usual ~18mA). However, I'm wondering if I'd be better off using a 4.5 or 6V supply (3x or 4x AA alkaline batteries), and use a buck/boost converter with a large-ish capacitor to provide the 9v...
Or, as the power draw on the logic circuit is so small.. maybe have 6x AA batteries to provide the full 9v, and a "centre tap" to take logic/led power off just three cells. That'd work, wouldn't it? And no need for any power regulation. Sure, 3 of the batteries would go flat marginally quicker than the other three, unless (over such small draws, they tend to even out).
The application, by the way, is a touch-sensor doorbell. The bell unit takes 850mA @ 9v as long as the coil is being driven, and my delay is currently 0.6s. The ATTiny85 drives it using 1 pin & a BC337 transistor, it also switches two LEDs, one a constant backlight LED, the other a "bell pressed" LED which takes over for a few seconds when the sensor fires. I'm happy with my circuit now (other than the power regulation for the 5v side), just need to finish making the hardware...