You are correct, Brian, about the minuscule current requirements of a varactor tuning system.
Many years ago, I saw a minimalist and effective way: it took a microcontroller line that was toggling something else, and used it to additionally drive a small transistor boost circuit. The duty cycle was not very consistent, but the voltage was post-regulated with a zener. Very clever!
So I would say that a simple joule thief with a zener regulator should suffice.