Terrible project idea - 9V battery drain prevention

I have a terrible idea.

I want to build a dedicated portable guitar out of a cheap hollow body guitar kit. Honestly, it's more of me just wanting something with effects and amplifier onboard to take around with me without needing a headphone amp or portable amp... the acoustic guitar convenience, in electric sound, if you will. (I already have a headphone amp and one of those Orange mini amps, if anybody is wondering).

C'mon, if I wanted real hollow body tone, I'd buy one of those $450 USD Gretsch guitars and call it good. This is just for fun. Please, hear me out first.

I'm having trouble figuring out how I'm going to wire the batteries. I plan to use onboard effects (three, to be exact), and they will be running off one 9V battery. The "cigar box amp" rig I'm looking at runs off another 9V battery.

The Amp has an on/off built into the volume pot (off -> on/volume). But it's wired for an input jack obviously. Will will drain the battery if I run the effects directly into the amp (bypassing the jack and just running the output wire from the effects to the amp jack input wire), even if the amp is off? I imagine I'd need a toggle switch (one or two...? I'm not sure) to control 9V battery drain to the effects and the amp when not in use.

Basically, my plan is:

pickups -> pickup toggle -> standard volume/tone -> onboard effects -> onboard amplifier

Can I wire a SPST ON/OFF toggle to each 9V battery in order to prevent standby battery consumption? Or is there a better way to do this? There will be no output or input jacks in the completed circuit, as this guitar is a fun project that will not be intended to be plugged in.

Any advice or input on the matter? I'm trying to find a workaround for this, and I feel like the solution is right in front of me...

Links:
GFS MODboards
Cigar Box Amp harness

Side note: I'm considering using a hollow body bass kit from The Fretwire instead, but I just think this would be better with the hollow body guitar kit instead. (Links for reference)

 

That’s something I didn’t even consider, running them in parallel together. So in order to do that with a SPST On/Off, would it basically be wiring the two 9V positive leads to the power input, and wiring the two negative leads to the SPST switch?

Is that pot modification one that would not drain battery life? I recall my mini amp that uses a similar on/off pot draining the battery when I left my cable plugged into the amp.