Elegant non-mechanical way to switch on battery-powered device the first time
Self latching power-up circuit: You seem to be overly concerned with the risks involved with a device holding itself on.   This is essentially how just about any device with only push-button normally-off switches works - extremely common and standard. eg any push-on push-off LED torch with a non latching switch, and those with multiple functions with multiple presses.   

Simple current transformer with half core: Core is inside case. Lay a conductor along case at correct location, pass current through cable and induce voltage in internal coupled coil. This is essentially a variant of NFC. I have transferred 1 Watt+ in this manner - from an insulated TPS coated wire to a ferrite 1/2 core. Power for eg FET turn on would be trivially easy.  

You can use a processor to hold the switch on or have a very simple latch so it is processor independent. 



Methods:

Capacitive power transfer can operate entirely successfully through a plastic case. Achievable power levels well in excess of "wake up" signals are possible. (Don't ask me how I know). 

You could use  vibration or ultrasonics with a piezo
A piezo could probably use "tap on the case" wake up signalling with a piezo pulse operating eg a MOSFET which requires only gate-capacitance charge-energy to turn on. As a bonus you could also use it for signalling to the device. A false-alarm start signal could be ignored if some sort of followup code was not sent immediately after the first signal. (As a real-world example: Coin mechanisms (illegally &amp; covertly modified) have been used to pass false input signals to slot machines by timing the coin insertion pattern to meet a preset code).
Don't ask me how I know :-).(No, it wasn't me.) )

Magnet-activated reed switches can be very rugged and reliable. I used one in a design (that ran to 100,000++ units) with some initial trepidation, but they performed even better than the specification and have been essentially trouble free in an 'anything goes' application. (Kicking the product down a flight of concrete stairs became a standard demonstration event. It was meant to "try to" survive ANY unreasonable thing that might reasonably happen to it including full immersion and all seasons exposure. The reed didn't feature in the "interesting field failures" list). A reed-switch has genuinely zero energy consumption when off. 

RF or NFC input requiring a coil and capacitor for resonance - or NFC with a coil only and less sensitivity has far more energy transfer capability than needed. It also could be used for signalling and even for external recharging if desired. 



In all cases the wake-up signal is required to provide minimal energy. A MOSFET gate is one possible very low power 'input'.