Put the piezo disk under the fingerboard. The Stagg 's fingerboard is flat on the downside (on an acoustic DB it is only flat at the upper half of of the hanging fingerboard, so you might want to put it a bit higher), so easy to glue there.
For testing get thin double sided sticky tape, like used to put paper photos in albums. Piezo disks are a bit tricky to solder, you might be able to get some with short soldered wires which are OK for testing. Be careful with the disks. Bending them might crack the thin piezo crystal and you need a new one. There are also piezo disks in plastic cases with short wires attached. They sound a bit darker but are better if you are afraid to break the disk.
The built-in electronics have the buffer, so nothing else necessary than a 1/8 T(R)S plug and a shielded cable. To access the electronics, you need to need to unscrew the electronics the the pots on. Try to identify the pickup sides by unplugging one of them and knocking at the bridge feet. You might need to loosen the strings and remove the bridge to knock at the piezo wire on both sides directly if you are not sure by knocking at the bridge feet. The T(R)S tip should be connected with the inner wire/red wire or the silver coating of the piezo disk, the shield of the T(R)S with the shielding of the wire/black or white wire or brass part of the piezo disk.
If you don't what that means, don't do it yourself unless you got the knowledge. It might work if someone a bit experienced in electronics can assist you.
Good luck and I would be interested in your experiences if you try doing that, so keep us informed here.