So I'm wondering what wire thickness is required for a homemade speaker level wire (200w amp head output over maybe 10cm)? And what connector type would be recommended for the wire type (I would like to connect 2 5cm wires together).
You probably want to make your cable resistance ≤ 1/10 of your speaker resistance which will most likely be 4 Ω or 8 Ω.
There are plenty of resistance calculators on line such as Omni Calculator which will do the calculations for you. A quick check for a 10 m loop (5 m out and back) with a 0.4 Ω target shows that 0.5 mm2 cable would do the job.