You have identified the problem correctly - white balance is the key.

Your camera does shoot in RAW format and this will probably be the easiest solution to your problem. By shooting in RAW format the white balance is not set in the camera, it is set later when you process the image on a pc. 

If you are willing then the place to start is to learn how to shoot in RAW format, and how to process your files to get the finished image you want. 

Did your camera come with software that will process the RAW files into Tiff's or Jpegs ?   
If it did great, you have got what you need. A quick read of the manual and a few trial shots should be enough to get you started. Once the files are in Tiff or Jpeg format you can treat them the same way as you would any image in photoshop. 

The subject you want to capture is ideal because I am guessing the contestants will be wearing white.  Their white suits will be your reference in processing the RAW file to get the colour balance correct.  The RAW processing software will have an eye dropper tool with which you can custom set a white balance.  You simply take this and click it on a part of the image which is white i.e. the contestants suits .   Voila - all the other colours will fall into place automatically . 

If you were shooting a scene with no white in it would need to introduce some by means of taking a test shot of a white card so you could get a white balance reading from that. 

hth

R

PS As a quick fix for images you already have shot in other formats use a photoshop levels or curves adjustment layer. You will see an eye dropper in the pop up adjustment window. The one you want this time is the grey one. Click it on the white clothing. Not as goood as shooting RAW, but a quick fix to make the best of what you have. Change layer blend mode to colour.

And every one said, 'If we only live,
We too will go to sea in a Sieve,---
To the hills of the Chankly Bore!'
Far and few, far and few, Are the lands where the Jumblies live;
Their heads are green, and their hands are blue, And they went to sea in a Sieve.

Edward Lear
http://www.nonsenselit.org/Lear/ns/jumblies.html