(grins) That 4-stroke engine looks to me like it is sitting on the red shelf under the work bench not on the red bike, or a photshop mock-up from a pic of the motor on the shelf and then dropped in the pic of the bike.
I guess he wanted to see how it looked but I can see right now that engine is way bigger than it looks in that pic and that red bottom mount plate is the bottom shelving you may have thought was a mount base.
I don't see a gas tank either.
But back to your post topic...
"Want to build my own Derringer"
A Derringer to me is a tiny pistol but I get the jest of the style of bike you are after.
Something like a 2-stroke chopper?
Or more like a retro board tracker with a 4-stroke?
That is a really old style Korean War M.A.S.H. era build but that is just the decoration.
What is important is you budget and needs.
1. Figure out how much you have to spend, then pick the bike for your needs first for the best daily riding experience for the practicality
of it, as it usually sucks picking a bike you have never even rode around first because it 'looks cool' and be stuck with how to motorize it and a miserable riding experience just so you 'look cool'.
2. What is your stature? Meaning weight, inseam, strength to pick the thing up, and ability to pedal dead weight or pull a pull starter.
3. What is your mechanical skill level and tools?
For example are you kid whose tools can fit in a small box and usually grab a crest wrench or pliers for most jobs?
Or are you mechanically inclined with ample tools and mechanical know-how?
You will see your power plant and bicycle options are narrowed down by a bunch to make how to proceed much easier.
If you start with those answers first you can build something you are proud of and enjoy riding within your budget and skill level.
Or not, that's just the questions I ask all my custom build customers first to fit their needs is all.