Would 4oz of watermelon extract be the right amount to add to the secondary or bottling bucket for a 5 gallon batch? I am in a wort transformation contest with a 5 gallon wheat.
4oz in 5 gallons for a what I imagine to be a fairly bland fruit extract doesn't sound like any problem. I've not tasted watermelon extract, but I do eat watermelon, and easily 4oz per serving. Watermelon has a subtle flavour.
With a wheat beer, the character is dominated by the esters produced by the yeast. Even though this is a competition with wort plus extras, don't underestimate how much you can do with just decent fermentation to get a balanced flavour profile. With a clean ferment, even a subtle addition will show through, but it's not going to be the entire definition of your beer - the clean ferment will do that.
So, even though you're in a competition with everyone brewing from the same malt, your beer isn't just a result of what you add - your process is what will make you stand out. It could be that many of your competitors ferment too cold or too warm and produce a beer that tastes very different.
To sum up, sure 4oz sounds fine, but be sure you reduce your water addition by 4oz if the extract is watery.