My intuition tells me that probably the most reliable and error-tolerant way would be to print the schematic on paper, cut it out, tape it to the plywood and then carefully saw along the outline
I was reading the post wondering if you would come to the same conclusion. Yes, I would think that this would be one of the easiest and most budget friendly ways to get your pattern onto the board.
Gluing the entire to your surface would not be required but everywhere near where you would be cutting would. If need be reverse the image before you print it and when you cut it the other side will be your intended design. Scraping the paper off after the fact wouldn't be too hard though.
Matthias Wandel uses that technique to make wooden gears (and other things...). Depending on the size of your design you could use something like Big Print which helps with accuracy on larger mediums.
As far as applying the paper template to the wood...
I always glue it on by putting a very thin coat of wood glue around the edge of the gear and then pressing the paper template on.
As long as the template it not going to move you should be able to cut out your design quickly and easily with hand tools like a coping / fret saw or even power tools like a bandsaw or jig saw. Routers with flush trim bits would also work everywhere except for fine detail areas.
The great marble music machine uses this technique as well (I know its another gears example but its really cool!)
Also for something small I strongly suggest using the same template for each one and not using a "good" one that you made as a template. Small errors will follow you that you might not see at first.