Round tube?
 

Would it be worth swopping some of the square tube in a Haynes chassis for CDS round tube?

Would there be a benefit in terms of weight and strength?

Perhaps in the bracing parts, that could quite easily be done in my garage. ie parts that don't have compound angles cut in them.

Thoughts?

Weigh for weight round tubing is stronger and lighter than square tubing (same size).
For example; 25mm diameter x 1.6mm thickness tube weight about 0.987 kg/meter and 25mm x 25mm x 1.6mm square tubing weight about 1.257 kg/meter, in other words, if you build the whole chassis from round tubing, it will weight about 25% lighter than a square tubing one and as said, be much stronger.

However, if you building a racer and need to save a few grams, you can do some of the bracing with round tube. My personal view is to either build square or round for simplicity and economics.

My Formula 27 chassis cross bracing was all round tube in the areas you mention and that was always regarded as a strong and good handling chassis.