We don’t know quite enough to design a davit for you.
What we can guess is that that 200 lbf end load can get a lot higher under sea if the dinghy fills with storm water and starts to bang around.
Another big issue is the attachment points. Everything about a boat is likely to be a structural element. Have you talked to the manufacturer (if they are still around)? Consulted with a marine architect?
What is significant deflection? An 1/8”?
Having said that, let’s try to address your problem as best we can.
The cantilevered beam loaded at the end deflects according to the following formula:
Deflection = load x length cubed / 3 times the elastic modulus times the section moment of inertia.
If we use 10,000,000 psi for the modulus, and 1/8” deflection, with your values we require a tube with a moment of inertia of: (Solving for ‘Inertia’)
(200 x 42 x 42 x 42) / (3 x 10,000,000 x .125) = 3.95 in^4
The moment of inertia of a hollow square tube = (outside to the fourth power minus inside to the fourth power) divided by 12.
X = the outside dimension and X-.25 is the inside.
I = 3.95 = (X^4 – (X-.25)^4)/12
Solve for X or find a shape in the catalog that equals or exceeds a Moment of Inertia of 3.95 inches^4.
A 4” x 4” tube fits this requirement with a moment of inertia of around 4.85. Now the peak stress level is only about 3500 psi at 200 lbs. This is within the yield strength and likely an adequate margin on safety.
You must decide in conjunction with your marine expert if the deflection of 1/8” can be exceeded and if you can provide adequate mounting.