Is it the shutter, or the mirror?
I'm not sure if mirror lockup work in high-speed continuous mode though.
On my 7D, there's a "silent shooting" mode on liveview, the shutter makes less sound, but one (or both) say not suitable for HSC. Read your manual, it's probably different to the 7D.
If it's just the mirror making the noise and the shutter isn't so bad (my experience is that the shutter on its own is no worse than a whisper a few meters away), then my solution would be to Manual Focus in live-view (or viewfinder focus then activate liveview), and let fly with HSC when he swings for the ball.
At least it's golf so subject is static, not running all over a field...