If you are not going to try to make that circuit into a stun gun (while I understand your reason probably more than most would, I really don't recommend it - I would not want to risk my life on it - it's far more likely just to annoy someone than hurt them, and get you killed when you could have escaped otherwise.) then there is lots of fun to be had with HV. Ionizers, ion-powered turbines and tiny moving models, moving arcs (I remember now - called 'Jacob's ladder'), arc cutters...
For safety though - add a chain of resistors to the output electrode to limit current to a mA or less. That way an accidental touch won't stop your heart!
I don't know about hot glue for HV - never tried it. Follow my points about minimum separation of
everything from the coil's output onwards.
You could use perfboard (as Sky_123 has) but fibreglass PCB would be better. It would be easy to make, even using rub-on transfers (like us oldies used to use) due to the large spacing and wide tracks.
When soldering, the idea is to make sure that no component lead ends show through the solder. These have sharp edges when cut and will cause corona loss: charge concentrates at a sharp points, causing electrons to jump on or off depending on polarity - this is how an ioniser works. So do 'poor' soldering, making sure to have a nice, round, shiny 'blob' of solder covering the ends. That's also why you must cut the lead before soldering, of course. Avoid sharp bends in the leads themselves, for the same (if not as critical - it's not as sharp) reason.
The component leads and tracks will need insulating - air is not a good insulator at high voltages.
Everything on the HV side will need coating.
If you are lucky enough to get a transformer that actually does give out five thousand volts, or use a flyback transformer, then I still say that the multiplier will die almost immediately. Old TV repair shops are good sources of flyback transformers, high voltage diodes and capacitors - I used to salvage mine from the local tip! More likely though any other transformer might give you a lot less voltage and the circuit might survive and produce a few thousand volts output. I ran my multipliers straight from 230Vac mains, so 'normal' diodes and mains-rated capacitors could be used. It takes a lot of them to get up to 10kV though.
Playing with a flyback transformer is an easy and fun way to make 10kV or more. That's how I started. Flyback transformers from TV's and monitors from about 15-20 years ago or younger are usually better than older ones. They already incorporate a diode and give around 25kV. Earlier ones are simpler (and still useful to play with) but have external multiplier components (useful parts) and only give about 8kV from the transformer itself.
One more thing to be cautious of: Ozone. It's good stuff up in the atmosphere, but very bad stuff down here. I forget the lethal concentration in air but it isn't much! Are you familiar with the 'electrical' smell behind old, tube television sets or old photocopiers and laser printers? That's a tiny amount of ozone from corona loss in the HV circuits. Pleasant in such tiny amounts, but people have been made very ill by working in small rooms with a photocopier before it was recognized as dangerous and the construction (and ventilation in rooms) improved.
My 25kV flyback generator, allowed to arc, produced so much that it made me feel really nauseous and dizzy with a minute or so of running it. I didn't know why - that's when I found out about ozone and how deadly it is. Be careful in there!
Here are some links to HV circuits:
http://www.powerlabs.org/flybackdriver.htm
**broken link removed**
Edit to add: I forgot to reiterate cleanliness when making the board. Make sure to clean off all traces of flux and grease (use a mild solvent or proper flux cleaner) before coating the board. Otherwise the HV will just leak through the flux and grease under the coating.